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arXiv · 1111.4616

Surfaces moving by powers of Gauss curvature

Ben Andrews·Xuzhong Chen
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Abstract

We prove that strictly convex surfaces moving by $K^{\alpha/2}$ become spherical as they contract to points, provided $\alpha$ lies in the range $[1,2]$. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.

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Ben Andrews, Xuzhong Chen. 2011-11-20. Surfaces moving by powers of Gauss curvature. https://arxiv.org/abs/1111.4616

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