Inverse Curvature Flows of Rotation Hypersurfaces  

作　　者：Yu Han JIN Xian Feng WANG Yong WEI 

机构地区：[1]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第11期1692-1708,共17页数学学报（英文版）

基　　金：Supported by the National Key R and D Program of China(Grant No.2020YFA0713100);National Natural Science Foundation of China(Grant Nos.11971244 and 11871283);Natural Science Foundation of Tianjin,China(Grant No.19JCQNJC14300);Research(Grant No.KY0010000052)from University of Science and Technology of China。

摘　　要：We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smooth,symmetric,strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces.We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value,and prove the long time existence and convergence of the flows.No second derivatives conditions are required on F.

关 键 词：Inverse curvature flow rotation hypersurface 

分 类 号：O186.1[理学—数学]