Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature

Abstract

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the ${\mathsf{CD}}^{\ast }(K,N)$ sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we show that a closed three-dimensional ${\mathsf{CD}}^{\ast }(2,3)$-Alexandrov space must be homeomorphic to a spherical space form or to the suspension of $\mathbb{R}{P}^2$. We then classify closed three-dimensional ${\mathsf{CD}}^{\ast }(0,3)$-Alexandrov spaces.

16 pages