Anisotropic inverse harmonic mean curvature flow  

作　　者：Jian LU 

机构地区：[1]Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032,China

出　　处：《Frontiers of Mathematics in China》2014年第3期509-521,共13页中国高等学校学术文摘·数学（英文）

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.

摘　　要：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.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.

关 键 词：Curvature flow parabolic equation asymptotic behavior 

分 类 号：O186.16[理学—数学] O343.8[理学—基础数学]