一类弹子轨迹凸域扩展辛容量的Brunn-Minkowski型不等式及长度估计

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-02-23 DOI:10.1007/s12188-023-00263-z

Rongrong Jin, Guangcun Lu

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引用次数: 0

摘要

本文首先将Artstein Avidan–Ostrover于2008年建立的有界凸域的Ekeland–Hofer–Zehnder辛容量的Brunn–Minkowski型不等式推广到作者最近基于一类Hamiltonian非周期边值问题构建的有界凸域的扩展辛容量。然后，我们引入了一类凸域中的非周期台球，并证明了与Artstein Avidan–Ostrover在2012年获得的凸域中周期台球的一些相应结果。

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

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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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.