Journal of Differential Geometry

Higher regularity of the inverse mean curvature flow

Gerhard Huisken and Tom Ilmanen

Full-text: Open access

Abstract

We prove higher regularity properties of inverse mean curvature flow in Euclidean space: A sharp lower bound for the mean curvature is derived for star-shaped surfaces, independently of the initial mean curvature. It is also shown that solutions to the inverse mean curvature flow are smooth if the mean curvature is bounded from below. As a consequence we show that weak solutions of the inverse mean curvature flow are smooth for large times, beginning from the first time where a surface in the evolution is star-shaped.

Article information

Source
J. Differential Geom., Volume 80, Number 3 (2008), 433-451.

Dates
First available in Project Euclid: 7 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1226090483

Digital Object Identifier
doi:10.4310/jdg/1226090483

Mathematical Reviews number (MathSciNet)
MR2472479

Zentralblatt MATH identifier
1161.53058

Citation

Huisken , Gerhard; Ilmanen, Tom. Higher regularity of the inverse mean curvature flow. J. Differential Geom. 80 (2008), no. 3, 433--451. doi:10.4310/jdg/1226090483. https://projecteuclid.org/euclid.jdg/1226090483


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