Energy capacity inequalities via an action selector

Details Energy capacity inequalities via an action selector Energy capacity inequalities via an action selector

2004-02-25

arxiv.org/abs/math/0402404v2

Mathematics

Differential Geometry

Besides minor changes, an appendix describing the constructions of the known action selectors is added. 27 pages, 1 figure, la

Scientific paper

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.

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