Discrete and Continuous Dynamical Systems · 2013 · 39 citations · 12 references
Natural SciencesMathematicsGeometryTopologyConvex GeometryEuclidean GeometryHyperbolic GeometryConjugate PointsCurvatureHyperbolic Surfaces
This paper deals with Hopf type rigidity for convex billiards onsurfaces of constant curvature. I prove that the only convexbilliard without conjugate points on the hyperbolic plane or on thehemisphere is a circular billiard.
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Riemannian tori without conjugate points are flat
Dmitri Burago, Sergei Ivanov · Geometric and Functional Analysis · 1994 · 111 citations
Convex billiards and a theorem by E. Hopf
Misha Bialy · Mathematische Zeitschrift · 1993 · 93 citations
Converse KAM theory for symplectic twist maps
Robert S. MacKay, James D. Meiss, J. Stark · Nonlinearity · 1989 · 80 citations