Mean curvature flow with surgery of mean convex surfaces in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

By S. Brendle, G. Huisken. Inventiones Mathematicae, 2013

59 citations recorded by the source corpus.

We define a notion of mean curvature flow with surgery for two-dimensional 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}$$\mathbb {R}^3$$\end{document} with positive mean curvature. Our construction relies on the earlier work of Huisken and Sinestrari in the higher dimensional case. One of the main ingredients in the proof is a new estimate for the inscribed radius established by the first author (Invent Math, 2015).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f538c2bc72779006638d5b03925756d5aa20f5a0