Anisotropic inverse harmonic mean curvature flow

We study the evolution of convex hypersurfaces [inline-graphic not available: see fulltext] with initial [inline-graphic not available: see fulltext] at a rate equal to H — f along its outer normal, where H is the inverse of harmonic mean curvature of [inline-graphic not available: see fulltext] 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 [inline-graphic not available: see fulltext] remains uniformly convex and expands to infinity as t → + ∞ and its scaling, [inline-graphic not available: see fulltext], converges to a sphere. In addition, the convergence result is generalized to the fully nonlinear case in which the evolution rate is logH-log f instead of H-f.