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arXiv · 2210.14286

Parabolic frequency for the mean curvature flow

Julius Baldauf·Tang-Kai Lee
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Abstract

This paper defines a parabolic frequency for solutions of the heat equation along homothetically shrinking mean curvature flows and proves its monotonicity along such flows. As a corollary, frequency monotonicity provides a proof of backwards uniqueness. Additionally, for solutions of more general parabolic equations on mean curvature flow shrinkers, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.

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Julius Baldauf, Tang-Kai Lee. 2022-10-25. Parabolic frequency for the mean curvature flow. https://arxiv.org/abs/2210.14286

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