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If a Minkowski billiard is projective, then it is the standard billiard
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In the recent paper [5] the first-named author proved that if a billiard in a convex domain in $\mathbb{R}^n$ is simultaneously projective and Minkowski, then it is the standard Euclidean billiard in an appropriate Euclidean structure. The proof was quite complicated and required high smoothness. Here we present a direct simple proof of this result which works in $C^1$-smoothness. In addition, we prove the semi-local and local versions of this result.
Bibliography: 15 titles.
Steklov Mathematical Institute
Title: If a Minkowski billiard is projective, then it is the standard billiard
Description:
In the recent paper [5] the first-named author proved that if a billiard in a convex domain in $\mathbb{R}^n$ is simultaneously projective and Minkowski, then it is the standard Euclidean billiard in an appropriate Euclidean structure.
The proof was quite complicated and required high smoothness.
Here we present a direct simple proof of this result which works in $C^1$-smoothness.
In addition, we prove the semi-local and local versions of this result.
Bibliography: 15 titles.
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