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arXiv · 1510.00655

Flow by the power of the Gauss curvature

Ben Andrews·Pengfei Guan·Lei Ni
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Abstract

We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $\alpha>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere.

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Ben Andrews, Pengfei Guan, Lei Ni. 2015-10-02. Flow by the power of the Gauss curvature. https://arxiv.org/abs/1510.00655

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