Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

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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.

Original languageEnglish
Pages (from-to)3903-3913
Number of pages11
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number9
DOIs
StatePublished - Sep 2013

Keywords

  • Billiards
  • Birkhoff conjecture
  • Conjugate points
  • Integrable systems

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