The size of the singular set in mean curvature flow of mean-convex sets

By B. White. 2000

250 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ff92b27e3e1ea3f48d19ce8af49ca86bcf89a463

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Robert Haslhofer
2. S. Brendle
3. Bruce Kleiner
4. G. Tian
5. G. Huisken
6. T. Colding
7. A. Neves
8. Jeff Cheeger

In Geometry and Topology

1. Robert Haslhofer
2. S. Brendle
3. Bruce Kleiner
4. G. Tian
5. G. Huisken
6. A. Neves
7. T. Colding
8. Jeff Cheeger

Citations in the corpus

• Translating solutions to Lagrangian mean curvature flow (2007, methodology): “In the first case, Brian White used his work on mean convex solutions to mean curvature flow [9] to show that no grim-reaper appears as the limit of a sequence of rescaled flows [10, Corollary 4].”
• Subsequent singularities in mean-convex mean curvature flow (2011, background): “The interior regularity and the interior behavior at t → ∞ are proved in [7].”
• EMBEDDED CONSTANT MEAN CURVATURE TORI IN THE THREE-SPHERE (2012, result): “The estimate was inspired by earlier work of Weimin Sheng and Xujia Wang [23] (see also [28]), who in the course of a detailed analysis of singularity profiles in mean curvature flow proved that for any embedded compact meanconvex hypersurface M moving under the mean curvature flow, there is a posit”
• Embedded minimal tori in S3 and the Lawson conjecture (2012, unknown): “By applying the maximum principle to a suitable function Wt(x, y) defined on M ×M , Andrews obtained a new proof of the noncollapsing estimate established earlier by Sheng and Wang [21] (see also [25]).”
• Convex solutions to the mean curvature flow (2004, background): “A key result in [26] is that a limit flow in F cannot be a hyperplane of multiplicity-two, from which it follows that the “grim reaper” xn+1 = log secx1 cannot be a limit flow in F ; see [22] and [27].”
• 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].”
• Noncollapsing in mean-convex mean curvature flow (2012, unknown): “(6) @Z @t D dHxhw; Hy y CHx xiC d(2) 2 .”
• Minimal 2-spheres in 3-spheres (2017, background): “We can consider the area functional on this space, and a minimal sphere is precisely 1In fact, White exhibited certain three-spheres (Theorem 4.5 in [31]) containing precisely 4 embedded minimal two-spheres. a critical point of this functional.”
• Mean Curvature Flow of Mean Convex Hypersurfaces (2013, methodology): “11, we obtain a new proof, also entirely without using Brakke flows (like everywhere else in the present paper) of White’s partial regularity theorem [36].”
• Uniqueness of two-convex closed ancient solutions to the mean curvature flow (2018, result): “Similar results for mean curvature flow were obtained in [12], [18], [19] assuming mean convexity and embeddedness.”
• A sharp bound for the inscribed radius under mean curvature flow (2013, background): “In a series of papers [16], [17], [18], B.”