Bounds for Minkowski Billiard Trajectories in Convex Bodies

Details Bounds for Minkowski Billiard Trajectories in Convex Bodies Bounds for Minkowski Billiard Trajectories in Convex Bodies

2011-11-09

arxiv.org/abs/1111.2353v2

Mathematics

Symplectic Geometry

Latex, 30 pages. A small typo in Section 3.3 was fixed, and thus Theorem 1.3 improved by a factor of 2

Scientific paper

In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide
several bounds and inequalities for the length of the shortest periodic
billiard trajectory in a smooth convex body in ${\mathbb R}^{n}$. Our results
hold both for classical billiards, as well as for the more general case of
Minkowski billiards.

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