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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
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: |
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| 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 |
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