Convexity estimates for flows by powers of the mean curvature
Felix Schulze (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We study the evolution of a closed, convex hypersurface in in direction of its normal vector, where the speed equals a power of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to , depending only on and , then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere. ...