The blow-up of the conformal mean curvature flow  

作　　者：Xingxiao Li Di Zhang 

机构地区：[1]College of Mathematics and Information Sciences,Henan Normal University,Xinxiang 453007,China

出　　处：《Science China Mathematics》2020年第4期733-754,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11671121,11171091 and 11371018)。

摘　　要：In this paper, we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space R^n. This kind of flow is a special case of a general modified mean curvature flow which is of various origination. As the main result, we prove a blow-up theorem concluding that, under the conformal mean curvature flow in R^n, the maximum of the square norm of the second fundamental form of any compact submanifold tends to infinity in finite time. Furthermore, we also prove that the external conformal forced mean curvature flow of a compact submanifold in R^n with the same pinched condition as Andrews-Baker's will be convergent to a round point in finite time.In this paper, we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space R^n. This kind of flow is a special case of a general modified mean curvature flow which is of various origination. As the main result, we prove a blow-up theorem concluding that, under the conformal mean curvature flow in R^n, the maximum of the square norm of the second fundamental form of any compact submanifold tends to infinity in finite time. Furthermore, we also prove that the external conformal forced mean curvature flow of a compact submanifold in R^n with the same pinched condition as Andrews-Baker’s will be convergent to a round point in finite time.

关 键 词：CONFORMAL mean CURVATURE flow CONFORMAL EXTERNAL FORCE BLOW-UP of the CURVATURE ROUND point 

分 类 号：O186[理学—数学]