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Shortest Minkowski billiard trajectories on convex bodies
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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.
Mathematics Subject Classification (2010) MSC 37C83
Title: Shortest Minkowski billiard trajectories on convex bodies
Description:
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.
Mathematics Subject Classification (2010) MSC 37C83.
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