Hyperbolic cone metrics and billiards

Hyperbolic cone metrics and billiards

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 associat...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2022-11, Vol.409, p.108662, Article 108662
Hauptverfasser: Erlandsson, Viveka, Leininger, Christopher J., Sadanand, Chandrika
Format: Artikel
Sprache:eng
Schlagworte:
Billiard
Cone metric
Geodesic current
Hyperbolic
Rigidity
Surface
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container_title Advances in mathematics (New York. 1965)
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creator Erlandsson, Viveka
Leininger, Christopher J.
Sadanand, Chandrika
description 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.
doi_str_mv 10.1016/j.aim.2022.108662
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source NORA - Norwegian Open Research Archives; Elsevier ScienceDirect Journals
subjects Billiard
Cone metric
Geodesic current
Hyperbolic
Rigidity
Surface
title Hyperbolic cone metrics and billiards
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