曲率二次衰减的完备流形的基本群

On the Fundamental Groups of Complete Manifolds with Lower Quadratic Curvature Decay

本文研究曲率二次衰减的完备黎曼流形,证明了若它的直径增长满足小的线性增长条件,则其基本群是有限生成的.

In this paper, we prove that a complete Riemannian manifold Mn with lower quadratic sectional curvature （or Ricci curvature） decay, if it has small linear diameter growth, then it has a finitely generated fundamental group.