Surfaces moving by powers of Gauss curvature

Details Surfaces moving by powers of Gauss curvature Surfaces moving by powers of Gauss curvature

2011-11-20

arxiv.org/abs/1111.4616v1

Mathematics

Differential Geometry

Scientific paper

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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