Work

If a Minkowski billiard is projective, then it is the standard billiard

Year: 2025

Type: article

Abstract: 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.

Source: Sbornik Mathematics

DOI: 10.4213/sm10182e

Authors: Alexey Antonovich Glutsyuk, Vladimir Sergeevich Matveev

Institutions: École Normale Supérieure de Lyon, National Research University Higher School of Economics, Centre National de la Recherche Scientifique, Moscow Institute of Physics and Technology, Unité de Mathématiques Pures et Appliquées, Friedrich Schiller University Jena

Language: English

Topic: Mathematics and Applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Friedrich-Schiller-Universität Jena, Deutsche Forschungsgemeinschaft, Ministry of Education and Science of the Russian Federation, Ministry of Science and Higher Education of the Russian Federation, Stony Brook University, Australian Research Council

Awards: G1107919517, G3463503224, Nijenhuisgeometrie: singuläre Punkte und Anwendungen, G5624822884, Polynomielle Integrabilität von natürlichen zweidimensionalen Hamiltonischen Systemen und deren Anwendungen

OpenAlex ID: W4413075550

FWCI: 5.372

Cites: 20

Cited by: 4

Related to: 10