Higher $P$-symmetric Ekeland-Hofer capacities

Abstract

This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for $P$-symmetric subsets in the standard symplectic space $({\mathbb{R}}^{2n},{\omega }_0)$, which is motivated by Long and Dong's study $P$-symmetric closed characteristics on $P$-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.

arXiv commentLatex, 21 pages

References in corpus (5)

• Symplectic embeddings and the lagrangian bidisk
• Estimating symplectic capacities from lengths of closed curves on the unit spheres
• Coisotropic Ekeland-Hofer capacities
• On the Ekeland-Hofer symplectic capacities of the real bidisc
• Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications