Displacement energy of unit disk cotangent bundles

Abstract

We give an upper bound of a Hamiltonian displacement energy of a unit disk cotangent bundle $D^{\ast }M$ in a cotangent bundle $T^{\ast }M$, when the base manifold $M$ is an open Riemannian manifold. Our main result is that the displacement energy is not greater than $Cr(M)$, where $r(M)$ is the inner radius of $M$, and $C$ is a dimensional constant. As an immediate application, we study symplectic embedding problems of unit disk cotangent bundles. Moreover, combined with results in symplectic geometry, our main result shows the existence of short periodic billiard trajectories and short geodesic loops.

Title slightly changed. Close to the version published online in Math Zeit

References in corpus (5)

• Symplectic topology of Mañé's critical values
• Symplectic embeddings of polydisks
• Metaphors in systolic geometry
• Symplectic capacity and short periodic billiard trajectory
• Symplectic homology of disc cotangent bundles of domains in Euclidean space

Cited by in corpus (1)

• On a Theorem by Schlenk