Harnack estimate for mean curvature flow on the sphere
Differential Geometry
2019-06-10 v4
Abstract
We consider the evolution of hypersurfaces on the unit sphere 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.
Keywords
Cite
@article{arxiv.1508.02821,
title = {Harnack estimate for mean curvature flow on the sphere},
author = {Paul Bryan and Mohammad N. Ivaki},
journal= {arXiv preprint arXiv:1508.02821},
year = {2019}
}
Comments
to appear in Asian J. Math