English

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 ρ(x)\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.

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}
}