A note on the representability of a certain Hamiltonian capacity

TL;DR

This paper proves a representation property for a specific Hamiltonian capacity in symplectic geometry, linking its value on certain sets to the boundary's action spectrum, thus deepening understanding of symplectic invariants.

Contribution

It establishes a new representation property for a Hamiltonian capacity on n, connecting it to the boundary's action spectrum in symplectic geometry.

Findings

Capacity value lies in the boundary's action spectrum

Representation property holds for sets with contact type boundary

Enhances understanding of symplectic invariants

Abstract

In this note we establish a representation property for a certain Hamiltonian capacity on $\R^{2n}$ with the standard symplectic structure. We demonstrate that the value of this capacity on an open set with a contact type boundary is an element of the action spectrum of the boundary.