Around the Funk metric and its billiards

Abstract: The Funk metric in the interior of a convex body is a lesser known relative of the projectively-invariant Hilbert metric, yet in some ways simpler and more natural. Starting with a few simple observations, we will explore some Funk-inspired generalizations of well-known results in the geometry of normed spaces and Minkowski billiards, such as Sch\"affer's dual girth conjecture and the Gutkin-Tabachnikov duality. I will also offer a Funk approach to the integrability of the hyperbolic billiard in a conic. Time permitting, I will discuss the volume of metric balls in Funk geometry, leading to a generalization of the Blaschke-Santalo inequality.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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