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 (R 2n , ω 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.