THE NATURE OF SINGULARITIES IN MEAN CURVATURE FLOW OF MEAN-CONVEX SETS

By B. White. 2002

252 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/344a443fd25b39f30d41a3a30b9ccede009a242a

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In Applied Mathematics

Citations in the corpus

Quantitative Stratification and the Regularity of Mean Curvature Flow (2012, result): “Our results build upon the deep regularity theory of Brian White [9, 10, 11, 12], which we briefly recall now: Given a Brakke flow M = {(Mt, t)} he considered the stratification of the singular set S ⇢M, (3) S ⇢ S(1) ⇢ · · · ⇢ S ⇢ S , where by definition X = (x, t) 2 Sj if and only if no tangent flo”
Ancient asymptotically cylindrical flows and applications (2019, background): “In [Whi03], the last author (see also [Ang13] and [HH16]) gave an example of a noncollapsed ancient, 1We recall that a mean-convex flow is α-noncollapsed [SW09, And12, HK17a] if at each point p ∈ Mt admits interior and exterior balls tangent at p of radius α/H(p).”
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].”
Translating solutions to Lagrangian mean curvature flow (2007, unknown): “(10) lim i→∞ λiH(1) ( {θ = a} ∩Bλ−1 i (λ −2 i e1) )”
Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields (2017, background): “One of the main research topics on mean curvature flow is the study of self-similar solutions particularly as models of singularities after suitable rescalings of the flow [27], [28], [50], [15], [16], [17].”
Translating solitons of the mean curvature flow (2015, background): “They are not only special solutions to the mean curvature flow equations, but they often occur as Type-II singularity of a mean curvature flow (see for example [1,2,9,24,25]).”
Convex ancient solutions of the mean curvature flow (2014, methodology): “Notice that the convexity assumption made in the current paper arises naturally since it was shown in [18, 22] that the rescaling of any singularity of a mean-convex solution of mean curvature flow is (weakly) convex.”
Subsequent singularities in mean-convex mean curvature flow (2011, background): “Incidentally, the assumption (*) that κ1/h is bounded below in a spacetime neighborhood of the singularity (both before and after the singularity) significantly simplifies the proofs in [8] in various places.”
Singularity Profile in the Mean Curvature Flow (2009, methodology): “The singularity profile has been studied by many authors [5, 8-13, 15, 21, 22], but in general it can be extremely complicated.”
Mean curvature flow with surgeries of two–convex hypersurfaces (2009, methodology): “White [28] has obtained convexity estimates for level-set solutions of mean curvature flow using methods from geometric measure theory.”
Crystalline Mean Curvature Flow of Convex Sets (2006, background): “In addition, singularities may appear during the evolution, and have been partially classified (see for instance [44, 45, 53, 3] and references therein).”
Ancient solutions of the mean curvature flow (2013, background): “Our proof is based on the recent estimates of Haslhofer-Kleiner [11], see also White [23, 24] and Huisken-Sinestrari [15, 16].”