# 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

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.

[1] U. Abresch, D. Gromoll. On complete manifolds with nonnegative Ricci curvature. Journal of AMS, 1990, 3(2): 355-374.

[2] P. Peterson. Riemannian geometry, GTM 171. New York: Springer-Verlag, 1998.

[3] S. Zhu. The comparison geometry of Ricci curvature. Comparison Geometry (MSRI Publications), 1997, 30: 221-262.

[4] 伍鸿熙, 沈纯理, 虞言林. 黎曼几何初步[M]. 北京: 北京大学出版社, 1989.

[5] 丘成桐, 孙理察. 微分几何[M]. 北京: 科学出版社, 1988.

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