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arXiv · 2310.05583

New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons

Wen-Qi Li
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Abstract

In this paper, we establish a new volume comparison theorem for a complete manifold with a function $\rho(x)$ 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.

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Wen-Qi Li. 2023-10-09. New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons. https://arxiv.org/abs/2310.05583

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