Journal of Geometry

, Volume 106, Issue 3, pp 483–501

Stability of the surface area preserving mean curvature flow in Euclidean space

Article

DOI: 10.1007/s00022-015-0260-8

Cite this article as:
Huang, Z. & Lin, L. J. Geom. (2015) 106: 483. doi:10.1007/s00022-015-0260-8

Abstract

The surface area preserving mean curvature flow is a mean curvature type flow with a global forcing term to keep the hypersurface area fixed. By iteration techniques, we show that the surface area preserving mean curvature flow in Euclidean space exists for all time and converges exponentially to a round sphere, if initially the L2-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex).

Mathematics Subject Classification

Primary 53C44 Secondary 58J35 

Copyright information

© Springer Basel AG 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe City University of New YorkStaten IslandUSA
  2. 2.The Graduate CenterThe City University of New YorkNew YorkUSA
  3. 3.Mathematics DepartmentUniversity of California, Santa CruzSanta CruzUSA

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