We give an upper bound of a Hamiltonian displacement energy of a unit disk
cotangent bundle DβM in a cotangent bundle TβM, 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.Comment: Title slightly changed. Close to the version published online in Math
Zei