关于Ricci曲率有下界的完备黎曼流形上的函数估计

On the Function Estimate on Complete Riemannian Manifolds with Ricci Curvature Bounded from Below

摘要: U. Abresch和D. Gromoll给出了一个关于Ricci曲率有下界的完备黎曼流形上函数估计的重要定理^[1]，本文利用更为精细的论述证明了将这个定理中的一个关键条件变弱后，定理的结论依然成立。

Abstract: U. Abresch and D. Gromoll found a theorem on the function estimate on complete Riemannian manifolds with Ricci curvature bounded from below^[1]. In this paper, it is proved that the conclusion of the theorem still holds when a crucial condition of the theorem is weakened.