调和映射的刘维尔型定理

A Liouville Type Theorem of Harmonic Maps

假设出发流形的径向截曲率Kr满足|Kr(x)|≤k(1-k)r2(x0,x),这里x0为极点,k为满足一定条件的常数,那么到任意象流形的能量慢发散的调和映射必是常映射.因而它是文献[3-4]中所提到的定理的推广.

Assuming the radial sectional curvature Kr of the target manifold satisfies ｜Kr（x）｜≤k（1-k） r2（x0,x）,where x0 is a pole,k is a constant satisfying some conditions,a harmonic map to any image manifold with slowly divergent energy must be constant.Then it improves the theorems of Reference raised.