Hyperbolic cone metrics and billiards

被引：0

作者：

Erlandsson, Viveka ^{[1
,2
]}

Leininger, Christopher J. ^{[3
]}

Sadanand, Chandrika ^{[4
]}

机构：

[1] Univ Bristol, Sch Math, Bristol, England

[2] UiT Arctic Univ Norway, Dept Math & Stat, Tromso, Norway

[3] Rice Univ, Dept Math, Houston, TX USA

[4] Bowdoin Coll, Dept Math, Brunswick, ME USA

来源：

ADVANCES IN MATHEMATICS | 2022年 / 409卷

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Hyperbolic; Cone metric; Surface; Billiard; Rigidity; Geodesic current; CODING CHAOTIC BILLIARDS; MARKED LENGTH-SPECTRUM; RIGIDITY; CURVATURE; SURFACES;

D O I：

10.1016/j.aim.2022.108662

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of hyperbolic polygons with the same symbolic coding for their billiard dynamics, and prove that generically this parameter space is a point. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：74

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