Translation surfaces with no convex presentation

Samuel Lelièvre; Barak Weiss

doi:10.1007/s00039-015-0349-0

Translation surfaces with no convex presentation

Samuel Lelièvre, Barak Weiss

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We give infinite lists of translation surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1,1), all surfaces in the eigenform loci (Formula presented.) or ε₁₆ have no strictly convex presentation, and that the list of surfaces with no convex presentations in (Formula presented.) is finite and consists of square-tiled surfaces. We prove the existence of non-lattice surfaces without strictly convex presentations in all of the strata (Formula presented.).

Original language	American English
Pages (from-to)	1902-1936
Number of pages	35
Journal	Geometric and Functional Analysis
Volume	25
Issue number	6
DOIs	https://doi.org/10.1007/s00039-015-0349-0
State	Published - 1 Dec 2015

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-015-0349-0

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abstract = "We give infinite lists of translation surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1,1), all surfaces in the eigenform loci (Formula presented.) or ε16 have no strictly convex presentation, and that the list of surfaces with no convex presentations in (Formula presented.) is finite and consists of square-tiled surfaces. We prove the existence of non-lattice surfaces without strictly convex presentations in all of the strata (Formula presented.).",

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AB - We give infinite lists of translation surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1,1), all surfaces in the eigenform loci (Formula presented.) or ε16 have no strictly convex presentation, and that the list of surfaces with no convex presentations in (Formula presented.) is finite and consists of square-tiled surfaces. We prove the existence of non-lattice surfaces without strictly convex presentations in all of the strata (Formula presented.).

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DO - 10.1007/s00039-015-0349-0

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JO - Geometric and Functional Analysis

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ER -

Translation surfaces with no convex presentation

Abstract

All Science Journal Classification (ASJC) codes

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