关键词: 非平凡调和函数, 双曲空间, 第二基本形式模长

Abstract: 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 submanifold was greater than -n(n-1)/4.

Key words: nontrivial harmonic function, length of the second fundamental form, hyperbolic space