Deforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow
| dc.creator | Wang, Mu-Tao | |
| dc.date | 2001-10-01 | |
| dc.date.accessioned | 2026-07-07T04:43:36Z | |
| dc.date.available | 2026-07-07T04:43:36Z | |
| dc.description | Let f:Σ_1 --> Σ_2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in Σ_1\times Σ_2. This article discusses a canonical way to deform f along area preserving diffeomorphisms. This deformation process is realized through the mean curvature flow of the graph of f in Σ_1\times Σ_2. It is proved that the flow exists for all time and the map converges to a canonical map. In particular, this gives a new proof of the classical topological results that O(3) is a deformation retract of the diffeomorphism group of S^2 and the mapping class group of a Riemman surface of positive genus is a deformation retract of the diffeomorphism group . | |
| dc.description | 13 pages, to be published in Mathematical Research Letter | |
| dc.identifier | https://arxiv.org/abs/math/0110020 | |
| dc.identifier | http://arxiv.org/abs/math/0110020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62296 | |
| dc.subject | Differential Geometry | |
| dc.title | Deforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow | |
| dc.type | text |