Serrin's type Problems in convex cones in Riemannian manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909453134069760 |
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| author | Araújo, Murilo Freitas, Allan Santos, Márcio Sindeaux, Joyce |
| author_facet | Araújo, Murilo Freitas, Allan Santos, Márcio Sindeaux, Joyce |
| contents | In this work, we discuss several results concerning Serrin's problem in convex cones in Riemannian manifolds. First, we present a rigidity result for an overdetermined problem in a class of warped products with Ricci curvature bounded below. As a consequence, we obtain a rigidity result for Einstein warped products. Next, we derive a soap bubble result and a Heintze-Karcher inequality that characterize the intersection of geodesic balls with cones in these spaces. Finally, we analyze the analogous ovedetermined problem for the drift Laplacian, where the ambient space is a cone in the Euclidean space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serrin's type Problems in convex cones in Riemannian manifolds Araújo, Murilo Freitas, Allan Santos, Márcio Sindeaux, Joyce Differential Geometry Analysis of PDEs In this work, we discuss several results concerning Serrin's problem in convex cones in Riemannian manifolds. First, we present a rigidity result for an overdetermined problem in a class of warped products with Ricci curvature bounded below. As a consequence, we obtain a rigidity result for Einstein warped products. Next, we derive a soap bubble result and a Heintze-Karcher inequality that characterize the intersection of geodesic balls with cones in these spaces. Finally, we analyze the analogous ovedetermined problem for the drift Laplacian, where the ambient space is a cone in the Euclidean space. |
| title | Serrin's type Problems in convex cones in Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2501.05551 |