RESEARCH ARTICLE

Anisotropic inverse harmonic mean curvature flow

  • Jian LU
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  • Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032, China

Received date: 18 Feb 2014

Accepted date: 17 Mar 2014

Published date: 24 Jun 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We study the evolution of convex hypersurfaces X(·,t) with initial X(,0)=θX0 at a rate equal to H-f along its outer normal, where H is the inverse of harmonic mean curvature of X(,t), X0 is a smooth, closed, and uniformly convex hypersurface. We find a θ>0 and a sufficient condition about the anisotropic function f, such that if θ>θ*,∗ , then X(,t) remains uniformly convex and expands to infinity as t→ +∞ and its scaling, X(,t)e-nt, converges to a sphere. In addition, the convergence result is generalized to the fully nonlinear case in which the evolution rate is log H-log f instead of H-f.

Cite this article

Jian LU . Anisotropic inverse harmonic mean curvature flow[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 509 -521 . DOI: 10.1007/s11464-014-0371-9

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