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  Higher regularity of the inverse mean curvature flow

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

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-1350-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-1353-7
Genre: Journal Article

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JDG-80-3-A3-huisken.pdf (Publisher version), 188KB
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 Creators:
Huisken, Gerhard1, Author              
Ilmanen, Tom2, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              
2External Organizations, ou_persistent22              

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 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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 Dates: 2008-11
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: eDoc: 398239
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Title: Journal of Differential Geometry
Source Genre: Journal
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Pages: - Volume / Issue: 80 (3) Sequence Number: - Start / End Page: 433 - 451 Identifier: ISSN: 0022-040X