Displacement energy of unit cotangent bundles

Details Displacement energy of unit cotangent bundles Displacement energy of unit cotangent bundles

2011-06-11

arxiv.org/abs/1106.2199v1

Mathematics

Symplectic Geometry

24pages, 3figures

Scientific paper

For given Riemannian manifold, we study the displacement energy of its unit cotangent bundle in its cotangent bundle. This displacement energy is obviously equal to infinity when the Riemannian manifold is closed. On the otherhand, our main result gives a nice upper bound of this displacement energy when the Riemannian manifold is noncompact. As an application, we prove the existence of a "short" periodic billiard trajectory on any compact Riemannian manifold with boundary.

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