关于高维Willmore问题  

On Willmore Problems for Higher Dimensions

作　　者：马志圣[1] 

机构地区：[1]四川师范大学数学系,成都610066

出　　处：《数学学报（中文版）》1999年第6期1035-1046,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：本文考虑高维欧氏空间中子流形Ｍ的一组有较好意义的共形不变的泛函．给出这些泛函通过Ｍ的Ｂｅｔｔｉ数的下界估计；给出对于管状超曲面的下界和对于双球环的下界以及达到这些下界的相应的子流形，并且证明对于管状超曲面所得的有关Ｂｅｔｔｉ数的下界是不精确的，方法是不适当的．给出类似Ｗｉｌｌｍｏｒｅ猜测的一些猜测．This paper consider a series of functionals with better sense of conformalinvariants of submanifold M in higher-dimensional Euclidean space. Gives estimate oflower bundles of these functionals in terms of Betti numbers of M; gives lower bundlesfor tubular hypersurfaces and lower bundles for twofold-sphere torns as well as givescorresponding submanifold which attains these lower bundles; furthermore, show theselower bundles relative to Betti numbers are not exact, this method is not appropriate.And gives some conjectures similarfto Willmore conjecture.

关 键 词：BETTI数 欧氏空间 子流形 Willmore问题 泛函 

分 类 号：O186.16[理学—数学]