Mathematics – Differential Geometry
Scientific paper
2004-02-25
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.
Frauenfelder Urs
Ginzburg Viktor
Schlenk Felix
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