Coisotropic Ekeland-Hofer capacities

Abstract

For subsets in the standard symplectic space $({\mathbb{R}}^{2n},{\omega }_0)$ whose closures are intersecting with coisotropic subspace ${\mathbb{R}}^{n,k}$ we construct relative versions of the Ekeland-Hofer capacities of the subsets with respect to ${\mathbb{R}}^{n,k}$, establish representation formulas for such capacities of bounded convex domains intersecting with ${\mathbb{R}}^{n,k}$. We also prove a product formula and a fact that the value of this capacity on a hypersurface $\mathcal{S}$ of restricted contact type containing the origin is equal to the action of a generalized leafwise chord on $\mathcal{S}$.

Published in: Proceedings of the Royal Society of Edinburgh Section A: Mathematics

References in corpus (6)

• Cup-length estimates for leaf-wise intersections
• Leafwise Coisotropic Intersections
• Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications
• Coisotropic Intersections
• Representation formula for symmetric symplectic capacity and applications
• Coisotropic Hofer-Zehnder capacities of convex domains and related results

Cited by in corpus (2)

• Coisotropic Hofer-Zehnder capacities of convex domains and related results
• Higher $P$-symmetric Ekeland-Hofer capacities