A note on Serrin's type problem on Riemannian manifolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929266570035200 |
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| author | Freitas, Allan Roncoroni, Alberto Santos, Márcio |
| author_facet | Freitas, Allan Roncoroni, Alberto Santos, Márcio |
| contents | In this paper, we deal with Serrin-type problems in Riemannian manifolds. First, we obtain a Heintze-Karcher inequality and a Soap Bubble result, with its respective rigidity, when the ambient space has a Ricci tensor bounded below. After, we approach a Serrin problem in bounded domains of manifolds endowed with a closed conformal vector field. Our primary tool, in this case, is a new Pohozaev identity, which depends on the scalar curvature of the manifold. Applications involve Einstein and constant scalar curvature spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19772 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on Serrin's type problem on Riemannian manifolds Freitas, Allan Roncoroni, Alberto Santos, Márcio Differential Geometry Analysis of PDEs In this paper, we deal with Serrin-type problems in Riemannian manifolds. First, we obtain a Heintze-Karcher inequality and a Soap Bubble result, with its respective rigidity, when the ambient space has a Ricci tensor bounded below. After, we approach a Serrin problem in bounded domains of manifolds endowed with a closed conformal vector field. Our primary tool, in this case, is a new Pohozaev identity, which depends on the scalar curvature of the manifold. Applications involve Einstein and constant scalar curvature spaces. |
| title | A note on Serrin's type problem on Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2305.19772 |