A Liouville Type Theorem of Harmonic Maps

Abstract:

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 ［3 4］ raised.