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November 2008 Higher regularity of the inverse mean curvature flow
Tom Ilmanen
J. Differential Geom. 80(3): 433-451 (November 2008). DOI: 10.4310/jdg/1226090483

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.

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Tom Ilmanen. "Higher regularity of the inverse mean curvature flow." J. Differential Geom. 80 (3) 433 - 451, November 2008. https://doi.org/10.4310/jdg/1226090483

Information

Published: November 2008
First available in Project Euclid: 7 November 2008

zbMATH: 1161.53058
MathSciNet: MR2472479
Digital Object Identifier: 10.4310/jdg/1226090483

Rights: Copyright © 2008 Lehigh University

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Vol.80 • No. 3 • November 2008
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