Optimal diameter estimates of three-dimensional Ricci limit spaces
Differential Geometry
2023-03-28 v2 Metric Geometry
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.
Cite
@article{arxiv.2302.09415,
title = {Optimal diameter estimates of three-dimensional Ricci limit spaces},
author = {Bo Zhu and Xingyu Zhu},
journal= {arXiv preprint arXiv:2302.09415},
year = {2023}
}
Comments
6 pages, a similar result for non-negative sectional curvature is added