Some Sphere Theorems in Linear Potential Theory
| Autor: | Borghini, Stefano, Mascellani, Giovanni, Mazzieri, Lorenzo |
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| Rok vydání: | 2017 |
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| Zdroj: | Trans. Amer. Math. Soc. 371 (2019) 7757-7790 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/7637 |
| Popis: | In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular bounded domain $\Omega \subset \mathbb{R}^n$, $n\geq 3$, we prove that if the mean curvature $H$ of the boundary obeys the condition $$ - \bigg[ \frac{1}{\text{Cap}(\Omega)} \bigg]^{\frac{1}{n-2}} \leq \frac{H}{n-1} \leq \bigg[ \frac{1}{\text{Cap}(\Omega)} \bigg]^{\frac{1}{n-2}} , $$ then $\Omega$ is a round ball. Comment: 41 pages |
| Databáze: | arXiv |
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