Energy capacity inequalities via an action selector
Differential Geometry
2007-05-23 v2 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.math/0402404,
title = {Energy capacity inequalities via an action selector},
author = {Urs Frauenfelder and Viktor Ginzburg and Felix Schlenk},
journal= {arXiv preprint arXiv:math/0402404},
year = {2007}
}
Comments
Besides minor changes, an appendix describing the constructions of the known action selectors is added. 27 pages, 1 figure, latex