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 $\mathcal{S}$.