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Volume-preserving flow by powers of the mth mean curvature

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Cabezas-Rivas, Esther and Sinestrari, Carlo (2010) Volume-preserving flow by powers of the mth mean curvature. Calculus of Variations and Partial Differential Equations, Vol.38 (No.3-4). pp. 441-469. doi:10.1007/s00526-009-0294-6

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Official URL: http://dx.doi.org/10.1007/s00526-009-0294-6

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Abstract

We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the mth mean curvature plus a volume preserving term, including the case of powers of the mean curvature or of the Gauss curvature. We prove that if the initial hypersurface satisfies a suitable pinching condition, the solution exists for all times and converges to a round sphere.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Calculus of Variations and Partial Differential Equations
Publisher: Springer
ISSN: 0944-2669
Official Date: July 2010
Dates:
DateEvent
July 2010Published
Volume: Vol.38
Number: No.3-4
Number of Pages: 29
Page Range: pp. 441-469
DOI: 10.1007/s00526-009-0294-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Leverhulme Trust (LT), DGI (Spain), FEDER, REAG, MIUR (Italy)
Grant number: MTM2007-65852, MTM2008-01013-E

Data sourced from Thomson Reuters' Web of Knowledge

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