Minimal submanifolds with small total scalar curvature in Euclidean space

Kodai Mathematical Journal

Keomkyo Seo¹ 

[1] School of Mathematics Korea Institute for Advanced Study

关键词: minimal submanifolds;    total scalar curvature;    gap theorem;    L2 harmonic forms;   

DOI  :  10.2996/kmj/1206454555

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(10)Let M be an n-dimensional complete minimal submanifold in Rn+p. Lei Ni proved that if M has sufficiently small total scalar curvature, then M has only one end. We improve the upper bound of total scalar curvature. We also prove that if M has the same upper bound of total scalar curvature, there is no nontrivial L2 harmonic 1-form on M.

【 授权许可】

Unknown