Inverse Curvature Flows of Rotation Hypersurfaces

作     者：Yu Han JIN Xian Feng WANG Yong WEI Yu Han JIN;Xian Feng WANG;Yong WEI

作者机构：School of Mathematical Sciences and LPMCNankai UniversityTianjin 300071P.R.China School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei 230026P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第11期

页      面：1692-1708页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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 

主　　题：Inverse curvature flow rotation hypersurface 

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 *** 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 *** second derivatives conditions are required on F.