A sharp bound for the inscribed radius under mean curvature flow

By S. Brendle. 2013

54 citations recorded by the source corpus.

We consider a family of embedded, mean convex hypersurfaces which evolve by the mean curvature flow. It follows from general results of White that the inscribed radius at each point on the hypersurface is at least $$\frac{c}{H}$$cH, where $$c$$c is a positive constant that depends only on the initial data. Andrews recently gave a new proof of that fact using the maximum principle. In this paper, we show that the inscribed radius is at least $$\frac{1}{(1+\delta ) \, H}$$1(1+δ)H at each point where the curvature is sufficiently large.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4474aa701638c623865879b3df81848287a8c508

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In Applied Mathematics

1. G. Huisken
2. S. Brendle
3. Robert Haslhofer
4. Hong-wei Xu
5. Burkhard Wilking
6. A. Malchiodi
7. J. Gu
8. S. Almaraz

In Geometry and Topology

1. G. Huisken
2. S. Brendle
3. Robert Haslhofer
4. Burkhard Wilking
5. Hong-wei Xu
6. A. Malchiodi
7. J. Gu
8. Ben Andrews

Citations in the corpus

• 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, methodology): “The following result was established in [3]:”