Spectral invariants and length minimizing property of Hamiltonian paths
Abstract
In this paper we provide a criterion for the quasi-autonomous Hamiltonian path (``Hofer's geodesic'') on arbitrary closed symplectic manifolds to be length minimizing in its homotopy class in terms of the spectral invariants that the author has recently constructed (math.SG/0206092). As an application, we prove that any autonomous Hamiltonian path on arbitrary closed symplectic manifolds is length minimizing in {\it its homotopy class} with fixed ends, when it has no contractible periodic orbits {\it of period one}, has a maximum and a minimum point which are generically under-twisted and all of its critical points are nondegenerate in the Floer theoretic sense. This is a sequel to the papers math.SG/0104243 and math.SG/0206092.
Cite
@article{arxiv.math/0212337,
title = {Spectral invariants and length minimizing property of Hamiltonian paths},
author = {Yong-Geun Oh},
journal= {arXiv preprint arXiv:math/0212337},
year = {2007}
}
Comments
The hypothesis in Theorem II is replaced by a more restricted condition of ``nondegeneracy in the Floer theoretic sense''