Parabolic Frequency for the Mean Curvature Flow
Copyright policy )Parabolic Frequency for the Mean Curvature Flow
Abstract This paper defines a parabolic frequency for solutions of the heat equation along homothetically shrinking mean curvature flows (MCFs) 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 MCF shrinkers, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.
- Massachusetts Institute of Technology United States
- Tamkang University Taiwan
Flows related to mean curvature, Quasilinear parabolic equations with mean curvature operator, homothetically shrinking mean curvature flows (MCFs)
Flows related to mean curvature, Quasilinear parabolic equations with mean curvature operator, homothetically shrinking mean curvature flows (MCFs)
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