-
Low Mach number limit of the global solution to the compressible Navier–Stokes system for large data in the critical Besov space Math. Ann. (IF 1.4) Pub Date : 2024-04-01 Mikihiro Fujii
Abstract In this paper, we consider the compressible Navier–Stokes system around the constant equilibrium states and prove the existence of a unique global solution for arbitrarily large initial data in the scaling critical Besov space provided that the Mach number is sufficiently small, and the incompressible part of the initial velocity generates the global solution of the incompressible Navier–Stokes
-
Infinite cyclic projective skew translation quadrangles do not exist Math. Ann. (IF 1.4) Pub Date : 2024-04-01 Koen Thas
Abstract In this paper we completely classify infinite cyclic projective skew translation quadrangles through a new approach first partially introduced in Thas (A question of Frohardt on 2-groups, skew translation quadrangles of even order and cyclic STGQs. Preprint (2022), 11 pp), and in the present paper (unexpectedly) adapted to the infinite case. Very surprisingly, these objects do not exist and
-
Extremal metrics on the total space of destabilising test configurations Math. Ann. (IF 1.4) Pub Date : 2024-04-01 Lars Martin Sektnan, Cristiano Spotti
Abstract We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples of manifolds admitting extremal Kähler metrics. It also shows for such metrics a new phenomenon of jumping of the complex structure along fibres.
-
Exhaustion functions and normal forms for proper maps of balls Math. Ann. (IF 1.4) Pub Date : 2024-03-22 Jiří Lebl
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at the origin leads to a normal form for rational proper maps of balls. The normal form of the map, which is up to composition with unitaries, takes the origin to
-
Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation Math. Ann. (IF 1.4) Pub Date : 2024-03-21 Qi Ding, J. Jost, Y. L. Xin
For any \(\Lambda >0\), let \(\mathcal {M}_{n,\Lambda }\) denote the space containing all locally Lipschitz minimal graphs of dimension n and of arbitrary codimension m in Euclidean space \(\mathbb {R}^{n+m}\) with uniformly bounded 2-dilation \(\Lambda \) of their graphic functions. In this paper, we show that this is a natural class to extend structural results known for codimension one. In particular
-
End-time regularity theorem for Brakke flows Math. Ann. (IF 1.4) Pub Date : 2024-03-21 Salvatore Stuvard, Yoshihiro Tonegawa
-
Non-pluripolar products on vector bundles and Chern–Weil formulae Math. Ann. (IF 1.4) Pub Date : 2024-03-20 Mingchen Xia
In this paper, we develop several pluripotential-theoretic techniques for singular metrics on vector bundles. We first introduce the theory of non-pluripolar products on holomorphic vector bundles on complex manifolds. Then we define and study a special class of singularities of Hermitian metrics on vector bundles, called \(\mathcal {I}\)-good singularities, partially extending Mumford’s notion of
-
Bi-Lipschitz embeddings of the space of unordered $$m$$ -tuples with a partial transportation metric Math. Ann. (IF 1.4) Pub Date : 2024-03-19 David Bate, Ana Lucía Garcia Pulido
Let \(\Omega \subset {\mathbb {R}}^n\) be non-empty, open and proper. This paper is concerned with \(Wb_p(\Omega )\), the space of p-integrable Borel measures on \(\Omega \) equipped with the partial transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on \(\partial \Omega \). Alternatively, we show that \(Wb_p(\Omega )\) is isometric to a subset of
-
Free boundary problems of the incompressible Navier–Stokes equations with non-flat initial surface in the critical Besov space Math. Ann. (IF 1.4) Pub Date : 2024-03-16 Takayoshi Ogawa, Senjo Shimizu
-
Semi-linear parabolic equations on homogenous Lie groups arising from mean field games Math. Ann. (IF 1.4) Pub Date : 2024-03-16 Paola Mannucci, Claudio Marchi, Cristian Mendico
The existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker–Planck equation and the Hamilton–Jacobi equation, are addressed. The anisotropic geometry of the state space plays a crucial role in our analysis and creates several issues that need to be overcome. Indeed, the ellipticity directions span, at any point, subspaces of dimension
-
A complete family of Alexandrov–Fenchel inequalities for convex capillary hypersurfaces in the half-space Math. Ann. (IF 1.4) Pub Date : 2024-03-14 Yingxiang Hu, Yong Wei, Bo Yang, Tailong Zhou
-
Completeness of derived interleaving distances and sheaf quantization of non-smooth objects Math. Ann. (IF 1.4) Pub Date : 2024-03-13 Tomohiro Asano, Yuichi Ike
-
Linear stability of compact shrinking Ricci solitons Math. Ann. (IF 1.4) Pub Date : 2024-03-10 Huai-Dong Cao, Meng Zhu
In this paper, we continue investigating the second variation of Perelman’s \(\nu \)-entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in Cao and Zhu (Math Ann 353(3):747–763, 2012), as well as the more recent work in Mehrmohamadi and Razavi (arXiv:2104.08343, 2021), and obtain a necessary and sufficient condition for a compact shrinking Ricci soliton
-
Relative entropy inequality for capillary fluids with density dependent viscosity and applications Math. Ann. (IF 1.4) Pub Date : 2024-03-07 Matteo Caggio, Donatella Donatelli
We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak–strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.
-
The stationary Gierer–Meinhardt system in the upper half-space: existence, nonexistence and asymptotics Math. Ann. (IF 1.4) Pub Date : 2024-03-07 Marius Ghergu
-
Intersection theoretic inequalities via Lorentzian polynomials Math. Ann. (IF 1.4) Pub Date : 2024-03-05 Jiajun Hu, Jian Xiao
We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersection theoretic inequalities, which we call rKT property, with respect to m-positive classes and Schur classes. We also study its convexity variants—the geometric inequalities for m-convex functions on the sphere and convex
-
Determination of the density in a nonlinear elastic wave equation Math. Ann. (IF 1.4) Pub Date : 2024-03-04 Gunther Uhlmann, Jian Zhai
This is a continuation of our study (Uhlmann and Zhai in J Math Pures Appl 153:114–136, 2021) on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the displacement-to-traction map, including the density, under some natural geometric conditions on the wavespeeds.
-
Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature Math. Ann. (IF 1.4) Pub Date : 2024-02-29 Wenchuan Tian, Changliang Wang
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonnegative scalar curvature and some additional uniform geometric bounds should have a subsequence which converges in some sense to a limit space with some generalized notion of nonnegative scalar curvature. In this paper, we study the pre-compactness of a sequence of three dimensional warped product manifolds
-
Global well-posedness and interior regularity of 2D Navier–Stokes equations with stochastic boundary conditions Math. Ann. (IF 1.4) Pub Date : 2024-02-27 Antonio Agresti, Eliseo Luongo
-
Linear strands of multigraded free resolutions Math. Ann. (IF 1.4) Pub Date : 2024-02-27 Michael K. Brown, Daniel Erman
We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green’s Linear Syzygy Theorem.
-
Correction to: Finite type invariants of w-knotted objects II: tangles, foams and the Kashiwara–Vergne problem Math. Ann. (IF 1.4) Pub Date : 2024-02-26 Dror Bar-Natan, Zsuzsanna Dancso
-
Asymptotic expansions for partitions generated by infinite products Math. Ann. (IF 1.4) Pub Date : 2024-02-26 Walter Bridges, Benjamin Brindle, Kathrin Bringmann, Johann Franke
Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in \(\Lambda \subset {\mathbb {N}}\) (\(\gcd (\Lambda )=1\)) and good analytic properties of the corresponding zeta function, generalizing work of Meinardus. In this paper, we extend their work to prove asymptotic formulas if \(\Lambda \) is a multiset of integers and the zeta function has multiple poles
-
Ricci flow with Ricci curvature and volume bounded below Math. Ann. (IF 1.4) Pub Date : 2024-02-26
Abstract We show that a simply-connected closed four-dimensional Ricci flow whose Ricci curvature is uniformly bounded below and whose volume does not approach zero must converge to a \(C^{0}\) orbifold at any finite-time singularity, so has an extension through the singularity via orbifold Ricci flow. Moreover, a Type-I blowup of the flow based at any orbifold point converges to a flat cone in the
-
Galois cohomology and profinitely solitary Chevalley groups Math. Ann. (IF 1.4) Pub Date : 2024-02-25 Holger Kammeyer, Ryan Spitler
-
Hölder continuity of weak solutions to evolution equations with distributed order fractional time derivative Math. Ann. (IF 1.4) Pub Date : 2024-02-21 Adam Kubica, Katarzyna Ryszewska, Rico Zacher
We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersolutions and Hölder continuity of weak solutions to this problem. Our results substantially generalise analogous known results for the problem with single order fractional time derivative.
-
A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold Math. Ann. (IF 1.4) Pub Date : 2024-02-17 Satoshi Ishiwata, Hiroshi Kawabi
In the present paper, we prove that the \(C_{0}\)-semigroup generated by a Schrödinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also
-
On Sobolev spaces of bounded subanalytic manifolds Math. Ann. (IF 1.4) Pub Date : 2024-02-14 Guillaume Valette
We focus on the Sobolev spaces of bounded subanalytic submanifolds of \(\mathbb {R}^n\). We prove that if M is such a manifold then the space \(\mathscr {C}_0^\infty (M)\) is dense in \(W^{1,p}(M,\partial M)\) (the kernel of the trace operator) for all \(p\le \mathbf {p_{_M}}\), where \(\mathbf {p_{_M}}\) is the codimension in M of the singular locus of \( {\overline{M}}{\setminus } M\) (which is always
-
Curve shortening flow on Riemann surfaces with conical singularities Math. Ann. (IF 1.4) Pub Date : 2024-02-13 Nikolaos Roidos, Andreas Savas-Halilaj
-
Existence of conformal symplectic foliations on closed manifolds Math. Ann. (IF 1.4) Pub Date : 2024-02-03 Fabio Gironella, Lauran Toussaint
-
Classification of minimal immersions of conformally flat 3-tori and 4-tori into spheres by the first eigenfunctions Math. Ann. (IF 1.4) Pub Date : 2024-02-02 Ying Lü, Peng Wang, Zhenxiao Xie
-
Global solvability and cohomology of tube structures on compact manifolds Math. Ann. (IF 1.4) Pub Date : 2024-02-01
Abstract We introduce new techniques to study the differential complexes associated to tube structures on \(M \times \mathbb {T}^m\) of corank m, in which M is a compact manifold and \(\mathbb {T}^m\) is the m-torus. By systematically employing partial Fourier series, for complex tube structures, we completely characterize global solvability, in a given degree, in terms of a weak form of hypoellipticity
-
Slowly recurrent Collet–Eckmann maps on the Riemann sphere Math. Ann. (IF 1.4) Pub Date : 2024-02-01 Magnus Aspenberg
In this paper we study perturbations of rational Collet–Eckmann maps for which the Julia set is the whole sphere, and for which the critical set is allowed to be slowly recurrent. Generically, if each critical point is simple, we show that each such Collet–Eckmann map is a Lebesgue point of Collet–Eckmann maps in the space of rational maps of the same degree \(d \ge 2\). The same result holds in each
-
The asymptotic p-Poisson equation as $$p \rightarrow \infty $$ in Carnot-Carathéodory spaces Math. Ann. (IF 1.4) Pub Date : 2024-01-29 Luca Capogna, Gianmarco Giovannardi, Andrea Pinamonti, Simone Verzellesi
In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as \(p\rightarrow +\infty \) in Carnot-Carathéodory spaces. In particular, introducing a suitable notion of differentiability, extend the celebrated result of Bhattacharya et al. (Rend Sem Mat Univ Politec Torino Fascicolo Speciale 47:15–68, 1989) and we prove that limits of such solutions solve in the
-
Periods, power series, and integrated algebraic numbers Math. Ann. (IF 1.4) Pub Date : 2024-01-29 Tobias Kaiser
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the polynomial ring over the rationals and evaluate it at a rational number. We follow this path and close these algebraic power series under taking iterated antiderivatives
-
Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps Math. Ann. (IF 1.4) Pub Date : 2024-01-28
Abstract By revisiting Tian’s peak section method, we obtain a localization principle of the Bergman kernels on Kähler manifolds with complex hyperbolic cusps, which is a generalization of Auvray–Ma–Marinescu’s (Math Ann 379:51–1002, 2021) localization result Bergman kernels on punctured Riemann surfaces . Then we give some further estimates when the metric on the complex hyperbolic cusp is a Kähler–Einstein
-
Stein complements in compact Kähler manifolds Math. Ann. (IF 1.4) Pub Date : 2024-01-28 Andreas Höring, Thomas Peternell
Given a projective or compact Kähler manifold X and a (smooth) hypersurface Y, we study conditions under which \(X {\setminus } Y\) could be Stein. We apply this in particular to the case when X is the projectivization of the so-called canonical extension of the tangent bundle \(T_M\) of a projective manifold M with Y being the projectivization of \(T_M\) itself.
-
Projection constants for spaces of Dirichlet polynomials Math. Ann. (IF 1.4) Pub Date : 2024-01-24 A. Defant, D. Galicer, M. Mansilla, M. Mastyło, S. Muro
Given a frequency sequence \(\omega =(\omega _n)\) and a finite subset \(J \subset {\mathbb {N}}\), we study the space \({\mathscr {H}}_{\infty }^{J}(\omega )\) of all Dirichlet polynomials \(D(s):= \sum \nolimits _{n \in J} a_n e^{-\omega _n s}, \, s \in {\mathbb {C}}\). The main aim is to prove asymptotically correct estimates for the projection constant \(\varvec{\lambda }\big ({\mathscr {H}}_\infty
-
A priori estimates for solutions to equations of motion of an inextensible hanging string Math. Ann. (IF 1.4) Pub Date : 2024-01-24 Tatsuo Iguchi, Masahiro Takayama
-
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients Math. Ann. (IF 1.4) Pub Date : 2024-01-19 Claudia Garetto, Bolys Sabitbek
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in [25, 26]. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients. Well-posedness is proven in the very weak sense for systems with singularities with respect to the space variable or the time variable. Consistency with the classical theory is proven in the
-
Semialgebraic Calderón-Zygmund theorem on regularization of the distance function Math. Ann. (IF 1.4) Pub Date : 2024-01-19 Beata Kocel-Cynk, Wiesław Pawłucki, Anna Valette
We prove that, for any closed semialgebraic subset W of \({\mathbb {R}}^n\) and for any positive integer p, there exists a Nash function \(f:{\mathbb {R}}^n\setminus W\longrightarrow (0, \infty )\) which is equivalent to the distance function from W and at the same time it is \(\Lambda _p\)-regular in the sense that \(|D^\alpha f(x)|\le C d(x, W)^{1- |\alpha |}\), for each \(x\in {\mathbb {R}}^n{\setminus
-
Dynamics of extensible beams with nonlinear non-compact energy-level damping Math. Ann. (IF 1.4) Pub Date : 2024-01-16 E. H. Gomes Tavares, M. A. Jorge Silva, I. Lasiecka, Vando Narciso
This work is motivated by experimental studies (NASA Langley Research Center) of nonlinear damping mechanisms present in flight structures. It has been observed that the structures exhibit significant nonlinear damping effects which are functions of the energy of the system. The present work is devoted to the study of long-time dynamics to a class of extensible beams/plates featuring nonlocal nonlinear
-
A new construction of weak solutions to compressible Navier–Stokes equations Math. Ann. (IF 1.4) Pub Date : 2024-01-14 Nilasis Chaudhuri, Piotr B. Mucha, Ewelina Zatorska
We prove the existence of the weak solutions to the compressible Navier–Stokes system with barotropic pressure \(p(\varrho )=\varrho ^\gamma \) for \(\gamma \ge 9/5\) in three space dimension. The novelty of the paper is the approximation scheme that instead of the classical regularization of the continuity equation (based on the viscosity approximation \(\varepsilon \Delta \varrho \)) uses more direct
-
Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum Math. Ann. (IF 1.4) Pub Date : 2024-01-13 Xin Zhong, Xuan Zhou
We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density (\(\lambda =\rho ^\beta \)) on the whole two-dimensional (2D) plane. Under a geometric angle condition for the initial direction field, we show the global existence and uniqueness of strong solutions provided that \(\beta >\frac{4}{3}\). It should be noticed that there is no other restrictions
-
Exponential decay estimates for fundamental matrices of generalized Schrödinger systems Math. Ann. (IF 1.4) Pub Date : 2024-01-12 Joshua Isralowitz, Blair Davey
In this article, we investigate systems of generalized Schrödinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay estimates for them. The Schrödinger operators that we consider have leading coefficients that are bounded and uniformly elliptic, while the zeroth-order terms are
-
The triangulation complexity of elliptic and sol 3-manifolds Math. Ann. (IF 1.4) Pub Date : 2024-01-12 Marc Lackenby, Jessica S. Purcell
-
Just-likely intersections on Hilbert modular surfaces Math. Ann. (IF 1.4) Pub Date : 2024-01-11
Abstract In this paper, we prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic p. Specifically, let C, D be two proper curves inside a mod p Hilbert modular surface associated to a real quadratic field split at p. Suppose that the curves are generically ordinary, and that at least one of them is ample. Then, the set of points in
-
On the profinite rigidity of free and surface groups Math. Ann. (IF 1.4) Pub Date : 2024-01-11
Abstract Let S be either a free group or the fundamental group of a closed hyperbolic surface. We show that if G is a finitely generated residually-p group with the same pro-p completion as S, then two-generated subgroups of G are free. This generalises (and gives a new proof of) the analogous result of Baumslag for parafree groups. Our argument relies on the following new ingredient: if G is a re
-
Relative genus bounds in indefinite four-manifolds Math. Ann. (IF 1.4) Pub Date : 2024-01-10 Ciprian Manolescu, Marco Marengon, Lisa Piccirillo
-
Winding of geodesic rays chosen by a harmonic measure Math. Ann. (IF 1.4) Pub Date : 2024-01-09 Timothée Bénard
-
Optimization problems on nodes of Sturm–Liouville operators with $$L^p$$ potentials Math. Ann. (IF 1.4) Pub Date : 2024-01-06 Jifeng Chu, Gang Meng, Feng Wang, Meirong Zhang
-
Convergence of Bergman measures towards the Zhang measure Math. Ann. (IF 1.4) Pub Date : 2024-01-05 Sanal Shivaprasad
-
Optimal $$L^2$$ extensions of openness type Math. Ann. (IF 1.4) Pub Date : 2024-01-03 Wang Xu, Xiangyu Zhou
We study the following optimal \(L^2\) extension problem of openness type: given a complex manifold M, a closed subvariety \(S\subset M\) and a holomorphic vector bundle \(E\rightarrow M\), for any \(L^2\) holomorphic section f defined on some open neighborhood U of S, find an \(L^2\) holomorphic section F on M such that \(F|_S = f|_S\), and the \(L^2\) norm of F on M is optimally controlled by the
-
Near optimal $$L^p\rightarrow L^q$$ estimates for euclidean averages over prototypical hypersurfaces in $$\mathbb {R}^3$$ Math. Ann. (IF 1.4) Pub Date : 2024-01-03
Abstract We find the precise range of (p, q) for which local averages along graphs of a class of two-variable polynomials in \(\mathbb {R}^3\) are of restricted weak type (p, q), with hypersurfaces equipped with Euclidean surface measure. We derive these results using non-oscillatory, geometric methods, for a model class of polynomials bearing a strong connection to the general real-analytic case.
-
On the large genus asymptotics of psi-class intersection numbers Math. Ann. (IF 1.4) Pub Date : 2024-01-01 Jindong Guo, Di Yang
Abstract Based on an explicit formula of the generating series for the n-point psi-class intersection numbers (cf. Bertola et al. Physica D 327:30–57, 2016), we give a novel proof of a conjecture of Delecroix et al. in (Duke Math J 170:2633–2718, 2021) regarding the large genus uniform leading asymptotics of the psi-class intersection numbers. We also investigate polynomiality phenomenon in the large
-
On Nash’s conjecture for models of viscous, compressible, and heat conducting fluids Math. Ann. (IF 1.4) Pub Date : 2023-12-28 Eduard Feireisl, Huanyao Wen, Changjiang Zhu
We show a new blow up criterion for regular solutions of the Navier–Stokes–Fourier system in terms of uniform bounds on the density and integral bounds on the absolute temperature. In comparison with the existing results, we remove the technical conditions relating the values of the shear and bulk viscosity coefficients. The result can be seen as a rigorous justification of Nash’s conjecture concerning
-
Bounds for Kloosterman sums on $$\textrm{GL}(n)$$ Math. Ann. (IF 1.4) Pub Date : 2023-12-27 Valentin Blomer, Siu Hang Man
This paper establishes power-saving bounds for Kloosterman sums associated with the long Weyl element for \(\textrm{GL}(n)\) for arbitrary \(n \geqslant 3\), as well as for another type of Weyl element of order 2. These bounds are obtained by establishing an explicit representation as exponential sums. As an application we go beyond Sarnak’s density conjecture for the principal congruence subgroup
-
How far apart can the projection of the centroid of a convex body and the centroid of its projection be? Math. Ann. (IF 1.4) Pub Date : 2023-12-27 Sergii Myroshnychenko, Kateryna Tatarko, Vladyslav Yaskin
-
Picard theorems for moduli spaces of polarized varieties Math. Ann. (IF 1.4) Pub Date : 2023-12-26
Abstract As a result of our study of the hyperbolicity of the moduli space of polarized manifold, we give a general big Picard theorem for a holomorphic curve on a log-smooth pair (X, D) such that \(W=X\setminus D\) admits a Finsler pseudometric that is strongly negatively curved when pulled back to the curve. We show, by some refinements of the classical Viehweg–Zuo construction, that this latter
-
On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations Math. Ann. (IF 1.4) Pub Date : 2023-12-25 Alberto Lastra, Stéphane Malek
A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic
-
Conformal metrics of the disk with prescribed Gaussian and geodesic curvatures Math. Ann. (IF 1.4) Pub Date : 2023-12-22 David Ruiz
This paper is concerned with the existence of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures. Being more specific, given nonnegative smooth functions \(K: \overline{\mathbb {D}}\rightarrow \mathbb {R}\) and \(h: \partial {\mathbb {D}}\rightarrow \mathbb {R}\), we consider the problem of finding a conformal metric realizing K and h as Gaussian and geodesic curvatures