Harnack estimate for mean curvature flow on the sphere

Paul Bryan; Mohammad N. Ivaki

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arXiv · 1508.02821

Harnack estimate for mean curvature flow on the sphere

Paul Bryan·Mohammad N. Ivaki

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Abstract

We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the mean curvature flow on the sphere.

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Paul Bryan, Mohammad N. Ivaki. 2015-08-12. Harnack estimate for mean curvature flow on the sphere. https://arxiv.org/abs/1508.02821

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