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

  • Author(s): Huang, Z
  • Lin, L
  • et al.
Abstract

© 2015, Springer Basel AG. The surface area preserving mean curvature flow is a mean curvaturetype flow with a global forcing term to keep the hypersurface areafixed. By iteration techniques, we show that the surface area preservingmean curvature flow in Euclidean space exists for all time and convergesexponentially to a round sphere, if initially the L2-norm of the traceless second fundamental form is small (but the initial hypersurface is notnecessarily convex).

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