A local regularity theorem for mean curvature flow

By F. Schulze, B. White. 2005

276 citations recorded by the source corpus.

This paper proves curvature bounds for mean curvature flows and other related flows in regions of spacetime where the Gaussian densities are close to 1.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e684723102f1d3b67286bca2553972faab680dd8

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers (2010, background): “10 in [20], 1 ≤ lim t↗T ∫ ρy0,T dμt < 2.”
Mean curvature flow with surgery of mean convex surfaces in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb (2013, background): “Furthermore, Brian White has obtained several breakthroughs in the analysis of the singularities of mean curvature flow; see [21], [22], [23], [24], [25], [26].”
Mean Curvature Flow in Higher Codimension: Introduction and Survey (2011, background): “Wang used the graphical condition in [Wan01b] to obtain long-time existence without a sign condition on S by methods related to White’s regularity theorem and then proved convergence of subsequences to minimal Lagrangian surfaces.”
Mean Curvature Flow of Mean Convex Hypersurfaces (2013, background): “The proof takes less than a page and vividly illustrates the efficiency of the ̨-Andrews condition in combination with the elementary local regularity theorem of White [39].”
A sharp lower bound for the entropy of closed hypersurfaces up to dimension six (2014, background): “[26] Y. Tonegawa,A second derivative Hölder estimate for weak mean curvature flow, Advances in Calculus of Variations 7 (2014), no. 1, 91–138 [27] B. White,Currents and flat chains associated to varifolds, with an application to mean curvature flow, Duke Math.”
On type-I singularities in Ricci flow (2010, methodology): “We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White’s partial regularity result for mean curvature flow [22].”
Subsequent singularities in mean-convex mean curvature flow (2011, unknown): “By the local regularity theorem in [9] (or by Brakke’s regularity theorem [1]), the convergence Uλ → U is smooth on \X , and thus κ1(Uλ, ·) h(Uλ, ·) → κ1(U, ·) h(U, ·) (3)”