As on arXiv
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.
Comments: 12 pages
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Parabolic frequency on Ricci flows
Topics Stability & uniqueness · Same author Julius Baldauf · Shared terms “parabolic frequency”, “backwards uniqueness”, “imply backwards”
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Parabolic frequency monotonicity for two nonlinear equations under Ricci flow
Shared terms “parabolic frequency”, “frequency monotonicity”, “parabolic equations”
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Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
Shared terms “parabolic frequency”, “frequency monotonicity”, “heat equation”
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Parabolic frequency monotonicity on the conformal Ricci flow
Shared terms “parabolic frequency”, “frequency monotonicity”, “heat equation”
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Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
Shared terms “parabolic frequency”, “frequency monotonicity”, “heat equation”
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Uniqueness of conical singularities for mean curvature flows
Topics Stability & uniqueness · Same author Tang-Kai Lee
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Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
Shared terms “parabolic frequency”, “heat equation”, “backward”
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A stable self-shrinking Möbius bundle in
Topics Stability & uniqueness · Same author Tang-Kai Lee · Shared terms “flow shrinkers”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.