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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
Gerhard Huisken (Sun,) studied this question.