Seminar in Real & Complex Geometry
Tuesday, 05.06.2012, 15:00-16:30,
building, room 210
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.