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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.01429 |
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| _version_ | 1866917793193000960 |
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| author | Park, Jiewon |
| author_facet | Park, Jiewon |
| contents | Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet certain conditions including bounds on the sectional curvature and covariant derivative of the Ricci curvature, as shown in the author's previous work \cite{P}. We also give explicit examples of warped product manifolds on which this assumption holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotonicity formulas and Hessian of the Green function Park, Jiewon Differential Geometry 53C20, 53C21, 53C24, 58J05 Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet certain conditions including bounds on the sectional curvature and covariant derivative of the Ricci curvature, as shown in the author's previous work \cite{P}. We also give explicit examples of warped product manifolds on which this assumption holds. |
| title | Monotonicity formulas and Hessian of the Green function |
| topic | Differential Geometry 53C20, 53C21, 53C24, 58J05 |
| url | https://arxiv.org/abs/2410.01429 |