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关于高维Willmore问题
引用本文:马志圣.关于高维Willmore问题[J].数学学报,1999,42(6):0-1046.
作者姓名:马志圣
作者单位:四川师范大学数学系,成都,610066
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.

关 键 词:子流形  共形不变量  Betti数  管状超曲面  双球环  Willmore问题
修稿时间::1997-04-0

On Willmore Problems for Higher Dimensions
Ma Zhisheng.On Willmore Problems for Higher Dimensions[J].Acta Mathematica Sinica,1999,42(6):0-1046.
Authors:Ma Zhisheng
Institution:Ma Zhisheng(Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China)(Fax: (028)4761994, E-mail: tomluo@nail.sc.cnind.net)
Abstract: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.
Keywords:Submanifold  Conformal invariant  Betti number  TUbular hypersurface  Twofold-sphere torns  Willmore problem  
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