Extensions of Bonnet-Myers' type theorems with the Bakry-Emery Ricci curvature

TL;DR

This paper extends classical Bonnet-Myers theorems using Bakry-Emery Ricci curvature, broadening the scope of geometric analysis results related to curvature bounds.

Contribution

It generalizes Bonnet-Myers type theorems by incorporating Bakry-Emery Ricci curvature, extending prior results by Calabi, Cheeger-Gromov-Taylor, and others.

Findings

Extended Bonnet-Myers theorems with Bakry-Emery Ricci curvature

Broadened geometric conditions for diameter bounds

Unified previous curvature-based results

Abstract

In this paper, we prove the extensions of Bonnet--Myers' type theorems obtained by Calabi and Cheeger--Gromov--Taylor via Bakry--Emery Ricci curvature, which generalize the results of \cite{FG, Lim1, Wan, Wang, WW, Wu}.