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arXiv · 1912.06623

Differential Harnack inequalities via Concavity of the arrival time

Theodora Bourni·Mat Langford
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Abstract

We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton's differential Harnack inequality for mean curvature flow and, more generally, Andrews' differential Harnack inequalities for certain "$α$-inverse-concave" flows.

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Theodora Bourni, Mat Langford. 2021-03-30. Differential Harnack inequalities via Concavity of the arrival time. https://arxiv.org/abs/1912.06623

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