Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-Émery Ricci curvature
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918454698704896 |
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| author | Ye, Jintao Zhu, Xiaohua |
| author_facet | Ye, Jintao Zhu, Xiaohua |
| contents | We prove a relative volume comparison theorem of Petersen-Wei for both $L^P$-bound of Bakry-Émery Ricci curvature and gradient of potential function. As an application, we give a modified proof for a volume comparison and monotonicity of Kähler-Ricci flow established in a recent work of Tian-Zhang-Zhang-Zhu-Zhu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17367 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-Émery Ricci curvature Ye, Jintao Zhu, Xiaohua Differential Geometry Primary 53C20, Secondary: 53C55, 58J05 We prove a relative volume comparison theorem of Petersen-Wei for both $L^P$-bound of Bakry-Émery Ricci curvature and gradient of potential function. As an application, we give a modified proof for a volume comparison and monotonicity of Kähler-Ricci flow established in a recent work of Tian-Zhang-Zhang-Zhu-Zhu. |
| title | Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-Émery Ricci curvature |
| topic | Differential Geometry Primary 53C20, Secondary: 53C55, 58J05 |
| url | https://arxiv.org/abs/2604.17367 |