Deforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow

dc.creatorWang, Mu-Tao
dc.date2001-10-01
dc.date.accessioned2026-07-07T04:43:36Z
dc.date.available2026-07-07T04:43:36Z
dc.descriptionLet 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.description13 pages, to be published in Mathematical Research Letter
dc.identifierhttps://arxiv.org/abs/math/0110020
dc.identifierhttp://arxiv.org/abs/math/0110020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62296
dc.subjectDifferential Geometry
dc.titleDeforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow
dc.typetext

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