Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914407584366592 |
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| author | Wu, Jia-Yong |
| author_facet | Wu, Jia-Yong |
| contents | In this paper, we prove the diameter comparison, the global weighted volume comparison and the splitting theorem in weighted manifolds when the infinity-Bakry-Emery Ricci curvature has a lower bound in the spectrum sense. Our results extend Antonelli-Xu's spectral Bonnet-Myers and Bishop-Gromov theorems, and Antonelli-Pozzetta-Xu's spectral splitting theorem to weighted manifolds. Our results are also some supplements of Chu-Hao's spectral diameter and global volume comparisons, and Yeung's spectral splitting theorem in weighted manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature Wu, Jia-Yong Differential Geometry Analysis of PDEs In this paper, we prove the diameter comparison, the global weighted volume comparison and the splitting theorem in weighted manifolds when the infinity-Bakry-Emery Ricci curvature has a lower bound in the spectrum sense. Our results extend Antonelli-Xu's spectral Bonnet-Myers and Bishop-Gromov theorems, and Antonelli-Pozzetta-Xu's spectral splitting theorem to weighted manifolds. Our results are also some supplements of Chu-Hao's spectral diameter and global volume comparisons, and Yeung's spectral splitting theorem in weighted manifolds. |
| title | Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2509.23182 |