双曲空间中极小子流形刚性的一些注记

Some Notes on Rigidity of Minimal Submanifolds in Hyperbolic Space

利用调和函数理论,考虑双曲空间中的完备极小子流形.证明了在第二基本形式模长平方上确界小于n(n-4)/4的条件下,或者子流形Ricci曲率的下确界大于-n(n-1)/4的条件下,子流形仅有一个端.

The author considered a complete minimal submanifold in hyperbolic space by using the theory of harmonic functions, and proved that there was only one end of the submanifold, if supremum of the length of the second fundamental form was less than n（n=4）/4, either infimum of Ricci curvature of the sub manifold was greater than -n（n=1）/4.