子流形平均曲率幂函数型泛函的变分（英文）  

Variation of power type functional about mean curvature of submanifolds

作　　者：刘进[1] Liu Jin(College of Systems Engineering,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学系统工程学院,湖南长沙410073

出　　处：《纯粹数学与应用数学》2018年第3期221-236,共16页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701565);湖南省自然科学基金(2016JJ3018);国防科技大学科研计划(ZK17-03-29)

摘　　要：假设φ:M^n→N^(n+p)是一般外围流形中的n维子流形,H^2是该子流形的平均曲率模长的平方,本文构造了H^2的幂函数型泛函M(n,r)=∫M(H^2)~rdv,其中r是一个实数.此泛函刻画了子流形与极小子流形的差异,并且与Willmore猜想有着密切联系.本文计算了该泛函的第一变分公式,并在单位球面中构造了该泛函临界点的一些例子.For an n-dimensional submanifold in a general real ambient manifoldφ:M^n→N^n+p,let H2 denote the square length of mean curvature vector ofφ.In this paper,we introduce one power type functional concerning H^2 as M(n;r)(φ)=∫M(H^2)^rdv,where r is a real number,which measures how derivationsφ(M)from a minimal submanifold and has a close relation with the well-known Willmore Conjecture.For this functional,the first variational equation is obtained.Moreover,in unit sphere,we construct a few examples of critical points.

关 键 词：平均曲率 极小子流形 Willmore猜想 临界点 

分 类 号：O186.1[理学—数学]