Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces  

作　　者：Li LEI Hongwei XU 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China. [2]Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第6期857-892,共36页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12071424,11531012,12201087).

摘　　要：Recently,Pipoli and Sinestrari[Pipoli,G.and Sinestrari,C.,Mean curvature flow of pinched submanifolds of CPn,Comm.Anal.Geom.,25,2017,799-846]initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space CPm.The purpose of this paper is to develop the work due to Pipoli and Sinestrari,and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective space.Namely,the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition,then the mean curvature flow converges to a round point in finite time,or converges to a totally geodesic submanifold as t→∞.Consequently,they obtain a differentiable sphere theorem for submanifolds in the complex projective space.

关 键 词：Mean curvature flow Submanifolds of arbitrary codimension Complex projective space Convergence theorem Differentiable sphere theorem 

分 类 号：O186[理学—数学]