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arXiv · 2310.07369

A differential Harnack inequality for noncompact evolving hypersurfaces

Stephen Lynch
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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.

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Stephen Lynch. 2023-10-11. A differential Harnack inequality for noncompact evolving hypersurfaces. https://arxiv.org/abs/2310.07369

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