摘要
我们学习凸的 hypersurfaces 的进化与在到沿着它的外部正常的 H f 的一个率平等者起始在 H 是泛音的逆的地方，意味着弯曲一光滑，关门，并且一致地凸的 hypersurface。我们发现一 *> 0 并且关于各向异性的功能 f 的一个足够的条件如果 >* ，那么仍然保持一致地凸并且作为 t + 并且它的可伸缩膨胀到无穷，，收敛到一个范围。另外，集中结果被概括到进化率是 logH 木头 f 而不是 H-f 的充分非线性的在盒子。
We study the evolution of convex hypersurfaces H（., t） with initial H（., 0） = 0H0 at a rate equal to H - f along its outer normal, where H is the inverse of harmonic mean curvature of H（., t）, H0 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 H（.,t） remains uniformly convex and expands to infinity as t →∞ and its scaling, H（-, 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.
基金
Acknowledgements The author would like to thank professor Huaiyu Jian for his comments and suggestions about this work. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11131005, 11271118, 11301034） and the Doctoral Programme Foundation of Institution of Higher Education of China.
