Year: 2018
Type: preprint
Abstract: In this note we study the higher dimensional convex billiards satisfying the so-called Gutkin property. A convex hypersurface $S$ satisfies this property if any chord $[p,q]$ which forms angle $δ$ with the tangent hyperplane at $p$ has the same angle $δ$ with the tangent hyperplane at $q$. Our main result is that the only convex hypersurface with this property in $\mathbf{R}^d, d\geq 3$ is a round sphere. This extends previous results on Gutkin billiards obtained in \cite{B0}.
Source: arXiv (Cornell University)
Author: Bialy, Michael
Institution: Tel Aviv University
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G7789814769
OpenAlex ID: W2974241968