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arXiv · 2005.12046

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

Joontae Kim·Seongchan Kim·Myeonggi Kwon
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Abstract

In this note we study the systoles of convex hypersurfaces in $\mathbb{R}^{2n}$ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

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Joontae Kim, Seongchan Kim, Myeonggi Kwon. 2020-05-25. Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities. https://arxiv.org/abs/2005.12046

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