Ben Andrews, Xuzhong Chen
Published 2011-11-20Version 1
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.
On maximum-principle functions for flows by powers of the Gauss curvature
Deforming a hypersurface by Gauss curvature and support function
Continuous family of surfaces translating by powers of Gauss curvature
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