Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Misha Bialy

doi:10.3934/dcds.2013.33.3903

Article Contents

2013, Volume 33, Issue 9: 3903-3913. Doi: 10.3934/dcds.2013.33.3903

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Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Misha Bialy^1,

1.
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University

Received: August 31, 2012

Revised: December 31, 2012

Published: August 2013

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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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Mathematics Subject Classification: Primary: 37J35, 37J50; Secondary: 37E40.

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