Parabolic frequency for the mean curvature flow

2022/10/25 by Julius Baldauf, Baldauf, Julius, Tang-Kai Lee +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.14286

openalex publication_date 2022/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On the rate of convergence of cylindrical singularity in mean curvature flow
• Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow

Related

• Parabolic frequency on Ricci flows
• Parabolic frequency on manifolds
• Parabolic frequency monotonicity on compact manifolds
• Generalized parabolic frequency on compact manifolds
• Uniqueness of compact tangent flows in Mean Curvature Flow