Displaying similar documents to “A logarithmic Gauss curvature flow and the Minkowski problem”

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 ℝ n + 1 in direction of its normal vector, where the speed equals a power k ≥ 1 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 1 , depending only on k and n , 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. ...