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  Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone

Marquardt, T. (2013). Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone. Journal of Geometric Analysis, 23(3), 1303-1313. doi:10.1007/s12220-011-9288-7.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-14AE-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-14AF-8
Genre: Journal Article

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JGeomAnal23_1303.pdf (Any fulltext), 228KB
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 Creators:
Marquardt, Thomas1, Author              
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: For a given convex cone we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicular. The evolution of those hypersurfaces inside the cone yields a nonlinear parabolic Neumann problem. We show that one can use the convexity of the cone to prove long time existence of this flow. Finally, we show that the hypersurfaces converge smoothly to a piece of the round sphere.

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 Dates: 2013
 Publication Status: Published in print
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 Identifiers: DOI: 10.1007/s12220-011-9288-7
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Title: Journal of Geometric Analysis
Source Genre: Journal
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Publ. Info: Boca Raton, FL : CRC Press
Pages: - Volume / Issue: 23 (3) Sequence Number: - Start / End Page: 1303 - 1313 Identifier: ISSN: 1050-6926
CoNE: /journals/resource/954926996194