Flow by mean curvature of convex surfaces into spheres

1984/01/01 by Gerhard Huisken · 18 citations
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.4310/jdg/1214438998

openalex publication_date 1984/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The motion of surfaces by their mean curvature has been studied by Brakke [1] from the viewpoint of geometric measure theory. Other authors investigated the corresponding nonparametric problem [2], [5], [9]. A reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal. In this paper we take a more classical point of view: Consider a compact, uniformly convex w-dimensional surface M = Mo without boundary, which is smoothly imbedded in R. Let Mo be represented locally by a diffeomorphism

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