双曲空间中子流形的刚性

Rigidity of submanifolds in hyperbolic space

研究双曲空间中具有常平均曲率的完备非紧子流形M,证明了当M的无迹张量?的L^n范数小于一个适当的常数时,其上不存在非平凡的L^2调和1-形式,并且M仅有一个端.

The complete non-compact submanifolds M with constant mean curvature is discussed in the hyperbolic space.If the L n norms of the traceless second fundamental forms?is less than a suitable constant,then there isn t nontrivial L^2 harmonic 1-forms.Furthermore,M has only end.