Spectral invariants and length minimizing property of Hamiltonian paths
| dc.creator | Oh, Yong-Geun | |
| dc.date | 2002-12-24 | |
| dc.date | 2003-12-09 | |
| dc.date.accessioned | 2026-07-07T04:54:03Z | |
| dc.date.available | 2026-07-07T04:54:03Z | |
| dc.description | 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. | |
| dc.description | The hypothesis in Theorem II is replaced by a more restricted condition of ``nondegeneracy in the Floer theoretic sense'' | |
| dc.identifier | https://arxiv.org/abs/math/0212337 | |
| dc.identifier | http://arxiv.org/abs/math/0212337 | |
| dc.identifier | Asian J. Math. 9 (2005), 1--18 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66093 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D35; 53D40 | |
| dc.title | Spectral invariants and length minimizing property of Hamiltonian paths | |
| dc.type | text |