2002/12/31 by Yong-Geun Oh
Mathematics · #math.SG #msc:53D35 #msc:53D40
published as Asian J. Math. 9 (2005), 1--18 · The hypothesis in Theorem II is replaced by a more restricted condition of ``nondegeneracy in the Floer theoretic sense''
arxiv created 2003/12/09 · arxiv updated 2009/11/30
In this paper we provide a criterion for the quasi-autonomous Hamiltonian path (``Hofer's geodesic'') on arbitrary closed symplectic manifolds (M,ω) to be length minimizing in its homotopy class in terms of the spectral invariants ρ(G;1) 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.