Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866909389693124608 |
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| author | Scheuer, Julian Xia, Chao |
| author_facet | Scheuer, Julian Xia, Chao |
| contents | We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem in spaceforms. Secondly, we prove stability theorems for Brendle's Heintze-Karcher inequality respectively constant mean curvature classification in a class of warped product spaces. The key tool is the first author's recent development of stability for level sets of a function under smallness of the traceless Hessian thereof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_02491 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds Scheuer, Julian Xia, Chao Differential Geometry Analysis of PDEs We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem in spaceforms. Secondly, we prove stability theorems for Brendle's Heintze-Karcher inequality respectively constant mean curvature classification in a class of warped product spaces. The key tool is the first author's recent development of stability for level sets of a function under smallness of the traceless Hessian thereof. |
| title | Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2207.02491 |