Spectral invariants and length minimizing property of Hamiltonian paths

dc.creatorOh, Yong-Geun
dc.date2002-12-24
dc.date2003-12-09
dc.date.accessioned2026-07-07T04:54:03Z
dc.date.available2026-07-07T04:54:03Z
dc.descriptionIn 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.
dc.descriptionThe hypothesis in Theorem II is replaced by a more restricted condition of ``nondegeneracy in the Floer theoretic sense''
dc.identifierhttps://arxiv.org/abs/math/0212337
dc.identifierhttp://arxiv.org/abs/math/0212337
dc.identifierAsian J. Math. 9 (2005), 1--18
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66093
dc.subjectSymplectic Geometry
dc.subject53D35; 53D40
dc.titleSpectral invariants and length minimizing property of Hamiltonian paths
dc.typetext

Files

Collections