Volume-preserving flow by powers of the mth mean curvature


DOI: 10.1007/s00526-009-0294-6

Cite this article as:
Cabezas-Rivas, E. & Sinestrari, C. Calc. Var. (2010) 38: 441. doi:10.1007/s00526-009-0294-6


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.

Mathematics Subject Classification (2000)

53C44 35K55 58J35 35B40 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly

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