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Shortest Minkowski billiard trajectories on convex bodies

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arxiv 2203.01802 v1 pith:GSI5KYOF submitted 2022-03-03 math.DS

Daniel Rudolf , Stefan Krupp This is my paper · ORCID
classification math.DS
keywords billiardminkowskitrajectoriesclosedfinslerbodiesconvexlength-minimizing
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abstract

We rigorously investigate closed Minkowski/Finsler billiard trajectories on $n$-dimensional convex bodies. We outline the central properties in comparison and differentiation from the Euclidean special case and establish two main results for length-minimizing closed Minkowski/Finsler billiard trajectories: one is a regularity result, the other is of geometric nature. Building on these results, we develop an algorithm for computing length-minimizing closed Minkowski/Finsler billiard trajectories in the plane.

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  1. Symplectic billiards as Minkowski billiards

    math.DS 2026-07 unverdicted novelty 6.5 of 10

    Minkowski and symplectic billiards are related by symplectic reduction, so symplectic billiards act as a square root of a symplectic Minkowski system, giving new even-period orbit bounds in higher dimensions.

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