Optimal diameter estimates of three-dimensional Ricci limit spaces

Abstract

In this note, we prove that positive scalar curvature can pass to three dimensional Ricci limit spaces of non-negative Ricci curvature when it splits off a line. As a corollary, we obtain an optimal Bonnet-Myers type upper bound. Moreover, we obtain a similar statement in all dimensions for Alexandrov spaces of non-negative curvature.

6 pages, a similar result for non-negative sectional curvature is added