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 Ω ⊂ Rn, n ≥ 3, we prove that if the mean curvature H of the boundary obeys the condition (Formula Presented) then Ω is a round ball.
Borghini, S., Mascellani, G., Mazzieri, L. (2019). Some sphere theorems in linear potential theory. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 371(11), 7757-7790 [10.1090/tran/7637].
Some sphere theorems in linear potential theory
Borghini, Stefano
;
2019
Abstract
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 Ω ⊂ Rn, n ≥ 3, we prove that if the mean curvature H of the boundary obeys the condition (Formula Presented) then Ω is a round ball.
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