If a Minkowski billiard is projective, then it is the standard billiard
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.
Authors
- Alexey Glutsyuk (ORCID: https://orcid.org/0000-0002-6432-2725)
- Vladimir S. Matveev (ORCID: https://orcid.org/0000-0002-2237-1422)
Institutions
- École Normale Supérieure de Lyon (FR)
- National Research University Higher School of Economics (RU)
- Centre National de la Recherche Scientifique (FR)
- Moscow Institute of Physics and Technology (RU)
- Unité de Mathématiques Pures et Appliquées (FR)
- Friedrich Schiller University Jena (DE)
Publication Details
- Journal
- Sbornik Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.4213/sm10182e
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
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