Energy capacity inequalities via an action selector

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

An action selector associates, in a suitable way, to each compactly supported Hamiltonian on a symplectic manifold an action value of the Hamiltonian. Action selectors are known to exist for a broad class of symplectic manifolds. We show how the existence of an action selector leads to sharp energy capacity inequalities between the Gromov width, the Hofer--Zehnder capacity, and the displacement energy. We also obtain sharp lower bounds for the smallest action of a closed characteristic on contact type hypersurfaces.
Besides minor changes, an appendix describing the constructions of the known action selectors is added. 27 pages, 1 figure, latex

Keywords

Differential Geometry, Symplectic Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70269

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402404
 http://arxiv.org/abs/math/0402404

Collections

arXiv