A differential Harnack inequality for noncompact evolving hypersurfaces
Differential Geometry
2023-10-12 v1 Analysis of PDEs
Abstract
We prove a differential Harnack inequality for noncompact convex hypersurfaces flowing with normal speed equal to a symmetric function of their principal curvatures. This extends a result of Andrews for compact hypersurfaces. We assume that the speed of motion is one-homogeneous, uniformly elliptic, and suitably 'uniformly' inverse-concave as a function of the principal curvatures. In addition, we assume the hypersurfaces satisfy pointwise scaling-invariant gradient estimates for the second fundamental form. For many natural flows all of these hypotheses are met by any ancient solution which arises as a blow-up of a singularity.
Cite
@article{arxiv.2310.07369,
title = {A differential Harnack inequality for noncompact evolving hypersurfaces},
author = {Stephen Lynch},
journal= {arXiv preprint arXiv:2310.07369},
year = {2023}
}