Higher regularity of the inverse mean curvature flow

Huisken, Gerhard; Ilmanen, Tom

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Higher regularity of the inverse mean curvature flow

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Huisken, Gerhard
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Huisken, G., & Ilmanen, T. (2008). Higher regularity of the inverse mean curvature flow. Journal of Differential Geometry, 80(3), 433-451.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-1350-D

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.