Curvature Decay Estimates of Graphical Mean Curvature Flow in Higher Codimensions

2014/01/16 by Knut Smoczyk, Smoczyk, Knut, Mao‐Pei Tsui +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1401.4154

openalex publication_date 2014/01/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces.

Citations

• An intrinsic rigidity theorem for minimal submanifolds in a sphere

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