# Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

20 Jul 2020  ·  Kim Joontae, Kim Seongchan, Kwon Myeonggi ·

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. read more

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Symplectic Geometry Dynamical Systems