English

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 Sn+1\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.

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