Seminar in Real & Complex Geometry

Tuesday, 05.06.2012, 15:00-16:30, Schreiber building, room 210

Michael Bialy, Tel Aviv University

Hopf rigidity for convex billiards on Hemisphere and Hyperbolic plane


Billiard ball motion inside a convex domain on constant curvature surface will be discussed. I shall prove that the only billiards with no conjugate points are circular billiards. This result has an important corollary saying that the only billiard ball maps which are "totally" integrable are of circular billiards. Proof of these results relies on isoperimetric inequality on the surface. No auxiliary knowledge is required.