New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909227459543040 |
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| author | Li, Wen-Qi |
| author_facet | Li, Wen-Qi |
| contents | In this paper, we establish a new volume comparison theorem for a complete manifold with a function $ρ(x)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons Li, Wen-Qi Differential Geometry In this paper, we establish a new volume comparison theorem for a complete manifold with a function $ρ(x)$ 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. |
| title | New Volume Comparison Results and Volume Growth Rigidity of Gradient Ricci Almost Solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2310.05583 |