Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Misha Bialy

doi:10.3934/dcds.2013.33.3903

Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Misha Bialy^*

^*Corresponding author for this work

School of Mathematical Sciences

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

19 Scopus citations

Abstract

This paper deals with Hopf type rigidity for convex billiards on surfaces of constant curvature. I prove that the only convex billiard without conjugate points on the hyperbolic plane or on the hemisphere is a circular billiard.

Original language	English
Pages (from-to)	3903-3913
Number of pages	11
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2013.33.3903
State	Published - Sep 2013

Keywords

Billiards
Birkhoff conjecture
Conjugate points
Integrable systems

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10.3934/dcds.2013.33.3903

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abstract = "This paper deals with Hopf type rigidity for convex billiards on surfaces of constant curvature. I prove that the only convex billiard without conjugate points on the hyperbolic plane or on the hemisphere is a circular billiard.",

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KW - Conjugate points

KW - Integrable systems

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Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Abstract

Keywords

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