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Linear isometries of noncommutative L0-spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-12 Aleksey Ber, Jinghao Huang, Fedor Sukochev
The description of (commutative and noncommutative) Lp$L_p$-isometries has been studied thoroughly since the seminal work of Banach. In the present paper, we provide a complete description for the limiting case, isometries on noncommutative L0$L_0$-spaces, which extends the Banach–Stone theorem and Kadison's theorem for isometries of von Neumann algebras. The result is new even in the commutative setting
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Path integrals and p-adic L-functions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-03 Magnus Carlson, Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Jeehoon Park, Hwajong Yoo
We prove an arithmetic ‘path integral’ formula for the inverse p $p$ -adic absolute values of Kubota–Leopoldt p $p$ -adic L $L$ -functions at roots of unity.
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On the Pohozaev identity for the fractional p-Laplacian operator in RN Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-03 Vincenzo Ambrosio
In this paper, we show the existence of a nontrivial weak solution for a nonlinear problem involving the fractional p $p$ -Laplacian operator and a Berestycki–Lions type nonlinearity. This solution satisfies a Pohozaev identity. Moreover, we prove that any sufficiently smooth solution fulfills the Pohozaev identity.
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Hausdorff dimension of plane sections and general intersections Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-02 Pertti Mattila
This paper extends some results of Mattila (J. Fractal Geom. 66 (2021) 389–401 and Ann. Acad. Sci. Fenn. A Math. 42 (2017) 611–620), in particular, removing assumptions of positive lower density. We give conditions on a general family P λ : R n → R m , λ ∈ Λ $P_{\lambda }:\mathbb {R}^n\rightarrow \mathbb {R}^m, \lambda \in \Lambda$ , of orthogonal projections which guarantee that the Hausdorff dimension
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Ramsey numbers and the Zarankiewicz problem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-02 David Conlon, Sam Mattheus, Dhruv Mubayi, Jacques Verstraëte
Building on recent work of Mattheus and Verstraëte, we establish a general connection between Ramsey numbers of the form r ( F , t ) $r(F,t)$ for F $F$ a fixed graph and a variant of the Zarankiewicz problem asking for the maximum number of 1s in an m $m$ by n $n$ 0 / 1 $0/1$ -matrix that does not have any matrix from a fixed finite family L ( F ) $\mathcal {L}(F)$ derived from F $F$ as a submatrix
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Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-01 Xiaoshang Jin
In this article, we investigate the rate at which the first Dirichlet eigenvalue of geodesic balls decreases as the radius approaches infinity. We prove that if the conformal infinity of an asymptotically hyperbolic Einstein manifold is of nonnegative Yamabe type, then the two-term asymptotic of the eigenvalues is the same as that in hyperbolic space.
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A note on quadratic forms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-04-01 Fabian Hebestreit, Achim Krause, Maxime Ramzi
For a field extension L / K $L/K$ we consider maps that are quadratic over L $L$ but whose polarisation is only bilinear over K $K$ . Our main result is that all such are automatically quadratic forms over L $L$ in the usual sense if and only if L / K $L/K$ is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic
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Narrow systems revisited Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-30 Chris Lambie-Hanson
We investigate connections between set-theoretic compactness principles and cardinal arithmetic, introducing and studying generalized narrow system properties as a way to approach two open questions about two-cardinal tree properties. The first of these questions asks whether the strong tree property at a regular cardinal κ ⩾ ω 2 $\kappa \geqslant \omega _2$ implies the singular cardinals hypothesis
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A criterion for nondensity of integral points Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-30 Natalia Garcia-Fritz, Hector Pasten
We give a general criterion for Zariski degeneration of integral points in the complement of a divisor D $D$ with n $n$ components in a variety of dimension n $n$ defined over Q $\mathbb {Q}$ or over a quadratic imaginary field. The key condition is that the intersection of the components of D $D$ is not well approximated by rational points, and we discuss several cases where this assumption is satisfied
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John Charlton Polkinghorne, 1930–2021 Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-29 David Fairlie
John Charlton Polkinghorne was very successful in two careers: as a theoretical physicist and as a theologian. As a physicist at Cambridge, he was one of the pioneers of applying complex variable theory to the study of properties of scattering amplitudes and contributed to the theory of strong (nuclear) interactions. In addition, he was a successful teacher, with many of his students gaining senior
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Hyperbolicity in non-metric cubical small-cancellation Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-29 Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise
Given a non-positively curved cube complex X $X$ , we prove that the quotient of π 1 X $\pi _1X$ defined by a cubical presentation ⟨ X ∣ Y 1 , ⋯ , Y s ⟩ $\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non-metric cubical small-cancellation conditions is hyperbolic provided that π 1 X $\pi _1X$ is hyperbolic. This generalises the fact that finitely presented classical C ( 7 ) $C(7)$ small-cancellation
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Smallest denominators Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-26 Jens Marklof
We establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J. Number Theory 19 (2023), 1405–1413] on the expected value of the smallest denominator of rational points in a randomly shifted interval of small length, and of the closely related 1977 Kruyswijk–Meijer conjecture recently proved by Balazard and Martin [Bull. Sci. Math. 187 (2023), Paper No. 103305]. We express
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The generalized Harer conjecture for the homology triviality Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-26 Wonjun Chang, Byung Chun Kim, Yongjin Song
The classical Harer conjecture states the stable homology triviality of the canonical embedding ϕ : B 2 g + 2 ↪ Γ g $\phi: B_{2g+2} \hookrightarrow \Gamma _{g}$ , which was proved by Song and Tillmann. The main part of the proof is to show that B ϕ + : B B ∞ + → B Γ ∞ + $\operatorname{B}\phi ^{+}: \operatorname{B}B_{\infty }^{+} \rightarrow \operatorname{B}\Gamma _{\infty }^{+}$ , induced from ϕ $\phi$
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K3 surfaces of Kummer type in characteristic two Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-26 Igor V. Dolgachev
We discuss K3 surfaces in characteristic two that contain the Kummer configuration of smooth rational curves.
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On the generalised Dirichlet divisor problem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-19 Chiara Bellotti, Andrew Yang
We improve unconditional estimates on Δk(x)$\Delta _k(x)$, the remainder term of the generalised divisor function, for large k$k$. In particular, we show that Δk(x)≪x1−1.889k−2/3$\Delta _k(x) \ll x^{1 - 1.889k^{-2/3}}$ for all sufficiently large fixed k$k$.
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Irredundant bases for the symmetric group Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-20 Colva M. Roney-Dougal, Peiran Wu
An irredundant base of a group G$G$ acting faithfully on a finite set Γ$\Gamma$ is a sequence of points in Γ$\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in G$G$, terminating at the trivial subgroup. Suppose that G$G$ is Sn$\operatorname{S}_{n}$ or An$\operatorname{A}_{n}$ acting primitively on Γ$\Gamma$, and that the point stabiliser is primitive in its natural
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Some convexity criteria for differentiable functions on the 2-Wasserstein space Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-17 Guy Parker
We show that a differentiable function on the 2-Wasserstein space is geodesically convex if and only if it is also convex along a larger class of curves which we call ‘acceleration-free’. In particular, the set of acceleration-free curves includes all generalised geodesics. We also show that geodesic convexity can be characterised through first- and second-order inequalities involving the Wasserstein
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Rigidity and vanishing theorems for submanifolds with free boundary in the unit ball Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-15 Entao Zhao, Shunjuan Cao
In this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology
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Generating the homology of covers of surfaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-14 Marco Boggi, Andrew Putman, Nick Salter
Putman and Wieland conjectured that if Σ∼→Σ$\widetilde{\Sigma }\rightarrow \Sigma$ is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzero elements of H1(Σ∼;Q)$\operatorname{H}_1(\widetilde{\Sigma };\mathbb {Q})$ under the action of lifts to Σ∼$\widetilde{\Sigma }$ of mapping classes on Σ$\Sigma$ are infinite. We prove that this holds
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Most likely balls in Banach spaces: Existence and nonexistence Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-11 Bernd Schmidt
We establish a general criterion for the existence of convex sets of fixed shape as, for example, balls of a given radius, of maximal probability on Banach spaces. We also provide counterexamples, showing that their existence may fail even in some common situations.
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Degrees of the stretched Kostka quasi-polynomials Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-13 Shiliang Gao, Yibo Gao
We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial Kλ,μ(N)$K_{\lambda,\mu }(N)$ in all classical types, improving a previous result by McAllister in slr(C)$\mathfrak {sl}_r(\mathbb {C})$. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky.
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Weak approximation of symmetric products and norm varieties Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-13 Sheng Chen, Ziyang Zhang
Let k$k$ be a number field. For a variety X$X$ over k$k$ that satisfies weak approximation with Brauer–Manin obstruction, we study the same property for smooth projective models of its symmetric products. Based on the same method, we also explore the property of weak approximation with Brauer–Manin obstruction for norm varieties.
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Almost spanning distance trees in subsets of finite vector spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-08 Debsoumya Chakraborti, Ben Lund
For d⩾2$d\geqslant 2$ and an odd prime power q$q$, consider the vector space Fqd$\mathbb {F}_q^d$ over the finite field Fq$\mathbb {F}_q$, where the distance between two points (x1,…,xd)$(x_1,\ldots ,x_d)$ and (y1,…,yd)$(y_1,\ldots ,y_d)$ is defined as ∑i=1d(xi−yi)2$\sum _{i=1}^d (x_i-y_i)^2$. A distance graph is a graph associated with a nonzero distance to each of its edges. We show that large subsets
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Upper bounds for Heilbronn's triangle problem in higher dimensions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Dmitrii Zakharov
We develop a new simple approach to prove upper bounds for generalizations of the Heilbronn's triangle problem in higher dimensions. Among other things, we show the following: for fixed d⩾1$d \geqslant 1$, any subset of [0,1]d$[0, 1]^d$ of size n$n$ contains
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Long-time existence of Brownian motion on configurations of two landmarks Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Karen Habermann, Philipp Harms, Stefan Sommer
We study Brownian motion on the space of distinct landmarks in Rd$\mathbb {R}^d$, considered as a homogeneous space with a Riemannian metric inherited from a right-invariant metric on the diffeomorphism group. As of yet, there is no proof of long-time existence of this process, despite its fundamental importance in statistical shape analysis, where it is used to model stochastic shape evolutions. We
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A shorter note on shorter pants Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Hugo Parlier
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best-known bound for closed surfaces.
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Perpetual cutoff method and discrete Ricci curvature bounds with exceptions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-05 Florentin Münch
One of the main obstacles regarding Bakry–Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds on parts of the graph. Moreover, we sharply upper bound the distance to the exception
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Small codes Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-04 Igor Balla
Determining the maximum number of unit vectors in Rr$\mathbb {R}^r$ with no pairwise inner product exceeding α$\alpha$ is a fundamental problem in geometry and coding theory. In 1955, Rankin resolved this problem for all α⩽0$\alpha \leqslant 0$, and in this paper, we show that the maximum is (2+o(1))r$(2+o(1))r$ for all 0⩽α≪r−2/3$0 \leqslant \alpha \ll r^{-2/3}$, answering a question of Bukh and
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Extreme values of L-functions of newforms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-03 Sanoli Gun, Rashi Lunia
In 2008, Soundararajan showed that there exists a normalized Hecke eigenform f $f$ of weight k $k$ and level one such that
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A vanishing theorem for varieties with finitely many solvable group orbits Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-28 Yiyu Wang
We reprove and generalize a result proved by Yavin that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a connected linear solvable group acts, including all spherical varieties.
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Localization of eigenfunctions in the Dirichlet beaker Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-28 G. Cardone, S. A. Nazarov, J. Taskinen
We construct the asymptotics of the eigenpairs of the Dirichlet problem for the Laplace operator in a thin-walled beaker and prove the localization effect for the functions near the bottom edge, a smooth closed contour, of the beaker. The main asymptotic terms are described by the eigenpairs of an ordinary differential equation on the edge and by the single eigenvalue belonging to the discrete spectrum
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Constructing Galois representations with prescribed Iwasawa λ-invariant Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-26 Anwesh Ray
Let p⩾5$p\geqslant 5$ be a prime number. We consider the Iwasawa λ$\lambda$-invariants associated to modular Bloch–Kato Selmer groups, considered over the cyclotomic Zp$\mathbb {Z}_p$-extension of Q$\mathbb {Q}$. Let g$g$ be a p$p$-ordinary cuspidal newform of weight 2 and trivial nebentype. We assume that the μ$\mu$-invariant of g$g$ vanishes, and that the image of the residual representation associated
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Rational Cuntz states peak on the free disk algebra Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-27 Robert T. W. Martin, Eli Shamovich
We apply realization theory of noncommutative (NC) rational multipliers of the Fock space, or free Hardy space of square–summable power series in several noncommuting variables to the convex analysis of states on the Cuntz algebra. We show, in particular, that a large class of Cuntz states that arise as the “NC Clark measures” of isometric NC rational multipliers are peak states for Popescu's free
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Character sums over sparse elements of finite fields Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-27 László Mérai, Igor E. Shparlinski, Arne Winterhof
We estimate mixed character sums of polynomial values over elements of a finite field F q r $\mathbb {F}_{q^r}$ with sparse representations in a fixed ordered basis over the subfield F q $\mathbb {F}_q$ . First we use a combination of the inclusion–exclusion principle with bounds on character sums over linear subspaces to get nontrivial bounds for large q $q$ . Then we focus on the particular case
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Exact Lagrangians in four-dimensional symplectisations Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-26 Georgios Dimitroglou Rizell
In this note, we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three-manifold. Note that any closed exact Lagrangian in the symplectisation is displaceable by a Hamiltonian isotopy. We also use positive loops to exhibit elementary examples of topologically linked Legendrians that are dynamically non-interlinked
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A fake Klein bottle with bubble Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-24 W. H. Mannan
We resolve the question of the existence of a finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble, but homotopically distinct to it.
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Axioms for the category of Hilbert spaces and linear contractions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-24 Chris Heunen, Andre Kornell, Nesta van der Schaaf
The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity, convexity or dimension.
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The automorphism group of the quantum grassmannian Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-23 S. Launois, T. H. Lenagan
The automorphism group of a quantised coordinate algebra is usually much smaller than that of its classical counterpart. Nevertheless, these automorphism groups are often very difficult to calculate. In this paper, we calculate the automorphism group of the quantum grassmannian in the case that the deformation parameter is not a root of unity. The main tool employed is the dehomogenisation equality
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Maximum principles and consequences for γ-translators in Rn+1 Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-23 José Torres Santaella
In this paper, we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flow, where the deformation speed is given by a homogeneous smooth symmetric positive function γ $\gamma$ defined in a symmetric open cone. The main result of this paper is about the uniqueness of γ $\gamma$ -translators in the class of complete graphs defined on a ball.
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On the ∞-topos semantics of homotopy type theory Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-22 Emily Riehl
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article, written as lecture notes to accompany a three-part mini course delivered at the Logic and Higher Structures workshop at CIRM-Luminy, attempt to survey the state of the art, first presenting Voevodsky's simplicial model
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On Pleijel's nodal domain theorem for the Robin problem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-21 Asma Hassannezhad, David Sher
We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular, we remove the restriction, imposed in previous work, that the Robin parameter be non-negative. We also improve the upper bound in the statement of the Pleijel theorem. In the particular example of a Euclidean ball, we calculate the explicit value of the Pleijel constant for a generic constant Robin parameter
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On quasicomplete k-surfaces in 3-dimensional space-forms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-20 Graham Smith
In the study of immersed surfaces of constant positive extrinsic curvature in space-forms, it is natural to substitute completeness for a weaker property, which we here call quasicompleteness. We determine the global geometry of such surfaces under the hypotheses of quasicompleteness. In particular, we show that, for k > Max ( 0 , − c ) $k>\text{Max}(0,-c)$ , the only quasicomplete immersed surfaces
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Decay rates for the 4D energy-critical nonlinear heat equation Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-19 Leonardo Kosloff, César J. Niche, Gabriela Planas
In this paper, we address the decay of solutions to the four-dimensional energy-critical nonlinear heat equation in the critical space H ̇ 1 $\dot{H}^1$ . Recently, it was proven that the H ̇ 1 $\dot{H}^1$ norm of solutions goes to zero when time goes to infinity, but no decay rates were established. By means of the Fourier Splitting Method and using properties arising from the scale invariance, we
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Frieze patterns over algebraic numbers Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Michael Cuntz, Thorsten Holm, Carlo Pagano
Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jørgensen and the first two authors. In this paper, we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic
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Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Alessandro Goffi
In this note, we prove interior a priori first- and second-order estimates for solutions of fully nonlinear degenerate elliptic inequalities structured over the vector fields of Carnot groups, under the main assumption that u $u$ is semiconvex along the fields. These estimates for supersolutions are new even for linear subelliptic inequalities in nondivergence form, whereas in the nonlinear setting
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On the effective version of Serre's open image theorem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Jacob Mayle, Tian Wang
Let E / Q $E/\mathbb {Q}$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod ℓ $\ell$ Galois representation ρ ¯ E , ℓ $\overline{\rho }_{E, \ell }$ of E $E$ is surjective for each prime number ℓ $\ell$ that is sufficiently large. Under the generalized Riemann hypothesis, we give an explicit upper bound on the largest prime ℓ $\ell$ , linear in the logarithm
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On the existence of products of primes in arithmetic progressions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-13 Barnabás Szabó
We study the existence of products of primes in arithmetic progressions, building on the work of Ramaré and Walker. One of our main results is that if q$q$ is a large modulus, then any invertible residue class mod q$q$ contains a product of three primes where each prime is at most q6/5+ε$q^{6/5+\epsilon }$. Our arguments use results from a wide range of areas, such as sieve theory or additive combinatorics
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On the geometry of rod packings in the 3-torus Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-07 Connie On Yu Hui, Jessica S. Purcell
Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that
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On Newton polytopes of Lagrangian augmentations Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-06 Orsola Capovilla-Searle, Roger Casals
This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly
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The higher regularity and decay estimates for positive solutions of fractional Choquard equations Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-06 Yinbin Deng, Xian Yang
In the paper, we study the higher regularity and decay estimates for positive solutions of the following fractional Choquard equations:
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Notes on overdetermined singular problems Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-06 Francesco Esposito, Berardino Sciunzi, Nicola Soave
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
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Nonautonomous double-phase equations with strong singularity and concave perturbation Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-05 Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Shuai Yuan
We consider a nonlinear Dirichlet problem driven by a nonautonomous double-phase differential operator and with a reaction consisting of a “strongly” singular term plus a concave perturbation. Using the Nehari method, we show the existence of a bounded strictly positive solution.
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q,t-Catalan measures Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-31 Ian Cavey
We introduce the q,t$q,t$-Catalan measures, a sequence of piece-wise polynomial measures on R2$\mathbb {R}^2$. These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and have many combinatorial similarities to the q,t$q,t$-Catalan numbers. Our main result realizes the q,t$q,t$-Catalan measures as a limit of higher q,t$q,t$-Catalan
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Derived equivalences of self-injective 2-Calabi–Yau tilted algebras Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-05 Anders S. Kortegaard
Consider a k$k$-linear Frobenius category E$\mathcal {E}$ such that the corresponding stable category C$\mathcal {C}$ is 2-Calabi–Yau, Hom-finite with split idempotents. Let l,m∈C$l,m\in \mathcal {C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras C(l,l)$\mathcal {C}(l,l)$ and C(m,m)$\mathcal {C}(m,m)$ are derived equivalent. Furthermore
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K-theory Soergel bimodules Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-01 Jens Niklas Eberhardt
We initiate the study of K$K$-theory Soergel bimodules, a global and K$K$-theoretic version of Soergel bimodules. We show that morphisms of K$K$-theory Soergel bimodules can be described geometrically in terms of equivariant K$K$-theoretic correspondences between Bott–Samelson varieties. We thereby obtain a natural categorification of K$K$-theory Soergel bimodules in terms of equivariant coherent sheaves
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Existence and rotatability of the two-colored Jones–Wenzl projector Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Amit Hazi
The two-colored Temperley–Lieb algebra 2TLR(sn)$2\,\mathrm{TL}_R({_{s}}{n})$ is a generalization of the Temperley–Lieb algebra. The analogous two-colored Jones–Wenzl projector JWR(sn)∈2TLR(sn)$\mathrm{JW}_R({_{s}}{n}) \in 2\,\mathrm{TL}_R({_{s}}{n})$ plays an important role in the Elias–Williamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability
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The upper bound of the harmonic mean of the Steklov eigenvalues in curved spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Hang Chen
Considering an n$n$-dimensional Riemannian manifold M$M$ whose sectional curvature is bounded above by κ⩽0$\kappa \leqslant 0$ and Ricci curvature is bounded below by (n−1)K$(n-1)K$, we obtain an upper bound of the harmonic mean of the first (n−1)$(n-1)$ nonzero Steklov eigenvalues for domains contained in M$M$. This can be viewed as certain isoperimetric inequality and generalizes the result on comparing
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Mather's regions of instability for annulus diffeomorphisms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Salvador Addas-Zanata, Fábio Armando Tal
Let f$f$ be a C1+ε$C^{1+\varepsilon }$ diffeomorphism of the closed annulus A$A$ that preserves orientation and the boundary components, and f∼$\widetilde{f}$ be a lift of f$f$ to its universal covering space. Assume that A$A$ is a Birkhoff region of instability for f$f$, and the rotation set of f∼$\widetilde{f}$ is a nondegenerate interval. Then there exists an open f$f$-invariant essential annulus
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Lifting problem for universal quadratic forms over totally real cubic number fields Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Daejun Kim, Seok Hyeong Lee
Lifting problem for universal quadratic forms asks for totally real number fields K$K$ that admit a positive definite quadratic form with coefficients in Z$\mathbb {Z}$ that is universal over the ring of integers of K$K$. In this paper, we show K=Q(ζ7+ζ7−1)$K=\mathbb {Q}(\zeta _7+\zeta _7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.
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On the logarithmic derivative of characteristic polynomials for random unitary matrices Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Fan Ge
Let U∈U(N)$U\in U(N)$ be a random unitary matrix of size N$N$, distributed with respect to the Haar measure on U(N)$U(N)$. Let P(z)=PU(z)$P(z)=P_U(z)$ be the characteristic polynomial of U$U$. We prove that for z$z$ close to the unit circle, P′P(z)$ \frac{P^{\prime }}{P}(z)$ can be approximated using zeros of P$P$ very close to z$z$, with a typically controllable error term. This is an analogue