Frontiers of Mathematics in China >
Anisotropic inverse harmonic mean curvature flow
Received date: 18 Feb 2014
Accepted date: 17 Mar 2014
Published date: 24 Jun 2014
Copyright
We study the evolution of convex hypersurfaces with initial at a rate equal to H-f along its outer normal, where H is the inverse of harmonic mean curvature of , X0 is a smooth, closed, and uniformly convex hypersurface. We find a and a sufficient condition about the anisotropic function f, such that if ∗ , then remains uniformly convex and expands to infinity as t→ +∞ and its scaling, , 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.
Key words: Curvature flow; parabolic equation; asymptotic behavior
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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