Extensions of the Bonnet-Myers Theorem
Differential Geometry
2025-09-03 v1
Abstract
In this paper, we present extensions of the classical Bonnet-Myers theorem for Riemannian manifolds with nonnegative Ricci curvature. Our results provide criteria for compactness and a method for estimating the diameter of such manifolds under general curvature conditions. As applications, we establish compactness theorems for manifolds whose Ricci curvature decays at polynomial or exponential rates.
Cite
@article{arxiv.2509.02126,
title = {Extensions of the Bonnet-Myers Theorem},
author = {Ronggang Li and Shaoqing Wang},
journal= {arXiv preprint arXiv:2509.02126},
year = {2025}
}