Representation formula for symmetrical symplectic capacity and applications

Rongrong Jin; Guangcun Lu

doi:10.3934/dcds.2020199

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2020, Volume 40, Issue 8: 4705-4765. Doi: 10.3934/dcds.2020199

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Representation formula for symmetrical symplectic capacity and applications

Rongrong Jin and
Guangcun Lu^,

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

^* Corresponding author: Guangcun Lu
^* Corresponding author: Guangcun Lu

Received: May 31, 2019

Revised: January 31, 2020

Published: May 2020

The second author is partially supported by the NNSF 11271044 of China

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Abstract

This is the second installment in a series of papers aimed at generalizing symplectic capacities and homologies. We study symmetric versions of symplectic capacities for real symplectic manifolds, and obtain corresponding results for them to those of the first [19] of this series (such as representation formula, a theorem by Evgeni Neduv, Brunn-Minkowski type inequality and Minkowski billiard trajectories proposed by Artstein-Avidan-Ostrover).

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Mathematics Subject Classification: Primary: 53D35, 53C23; Secondary: 70H05, 37J05, 57R17.

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