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Bounded geometry with no bounded pants decomposition

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Abstract

We construct a quasiconformally homogeneous hyperbolic Riemann surface—other than the hyperbolic plane—that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact boundary components, we construct a complete hyperbolic metric on the surface that has bounded geometry but does not admit a bounded pants decomposition.

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Author information

Authors and Affiliations

  1. The Graduate Center and Hunter College, City University of New York, New York, NY, 10016, USA

    Ara Basmajian

  2. Department of Mathematics, University of Luxembourg, L-4364, Esch-sur-Alzette, Luxembourg

    Hugo Parlier

  3. Department of Mathematics, Queens College, City University of New York, New York, NY, 11367, USA

    Nicholas G. Vlamis

Authors
  1. Ara Basmajian
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  2. Hugo Parlier
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  3. Nicholas G. Vlamis
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Corresponding author

Correspondence to Ara Basmajian.

Additional information

Supported by a grant from the Simons Foundation (359956, A.B.).

Supported by the Luxembourg National Research Fund OPEN grant O19/13865598.

Supported in part by PSC-CUNY Award # 63524-00 51.

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Basmajian, A., Parlier, H. & Vlamis, N.G. Bounded geometry with no bounded pants decomposition. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2558-9

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  • DOI: https://doi.org/10.1007/s11856-023-2558-9

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