New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons
Differential Geometry
2024-06-21 v4
Abstract
In this paper, we establish a new volume comparison theorem for a complete manifold with a function as the lower bound of the Bakry-Emery Ricci curvature. As applications, we obtain a new volume rigidity result of the gradient Ricci almost solitons. Furthermore, we extend the results of Cao and Zhou \cite{CZ} to shrinking gradient Ricci almost solitons and get the rigidity result with respect to the maximal volume growth.
Keywords
Cite
@article{arxiv.2310.05583,
title = {New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons},
author = {Wen-Qi Li},
journal= {arXiv preprint arXiv:2310.05583},
year = {2024}
}