Estimating symplectic capacities from lengths of closed curves on the unit spheres

Abstract

We improve the estimates for the Ekeland--Hofer--Zehnder capacity of convex bodies by Gluskin and Ostrover. In the course of our argument we show that a closed characteristic of minimal action on the boundary of a centrally symmetric convex body in ${\mathbb{R}}^{2n}$ must itself be centrally symmetric, with generalizations to some other types of symmetry.

Cited by in corpus (2)

• Higher $P$-symmetric Ekeland-Hofer capacities
• A note on the capacities of Lagrangian $p$-sum