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arXiv · 2302.12102

A Brunn-Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories

Rongrong Jin·Guangcun Lu
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Abstract

In this paper, we firstly generalize the Brunn-Minkowski type inequality for Ekeland-Hofer-Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan-Ostrover in 2008 to extended symplectic capacities of bounded convex domains constructed by authors based on a class of Hamiltonian non-periodic boundary value problems recently. Then we introduce a class of non-periodic billiards in convex domains, and for them we prove some corresponding results to those for periodic billiards in convex domains obtained by Artstein-Avidan-Ostrover in 2012.

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Rongrong Jin, Guangcun Lu. 2023-02-23. A Brunn-Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories. https://doi.org/10.1007/s12188-023-00263-z

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