Stability of the surface area preserving mean curvature flow in Euclidean space

2012/11/05 by Huang, Zheng, Lin, Longzhi
#53C44 (Primary) 58J35 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.0764

Abstract

We show that the surface area preserving mean curvature flow in Euclidean space exists for all time and converges exponentially to a round sphere, if initially the L²-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex).

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