Bounds for Minkowski Billiard Trajectories in Convex Bodies
By Shiri Artstein-Avidan, Y. Ostrover. 2011
76 citations recorded by the source corpus.
In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in ${\mathbb R}^{n}$. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.
Subfields: Applied Mathematics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/5acd7e8943c57e478e6d3a381e9ae6512712ca6b
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In Applied Mathematics
- Roman N. Karasev
- Y. Ostrover
- Shiri Artstein-Avidan
- Serge Tabachnikov
- Richard Evan Schwartz
- Anna Pratoussevitch
- Elisha Falbel
- Sergey G. Bobkov
In Molecular Biology
Citations in the corpus
- From symplectic measurements to the Mahler conjecture (2013, methodology): “1, were given only for the class of convex bodies with smooth boundary, they can naturally be generalised to the class of convex sets in R2n with non-empty interior (see [2]).”
- Billiards in ellipses revisited (2020, background): “It was noticed in [3] that minimal action of a billiard in Minkowski metric is related with Ekeland–Hofer–Zehnder capacity, which made it possible to apply symplectic geometry to convex geometry problems.”