We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open interval and the unit sphere. We also extend the result by replacing the Laplacian with the q-Laplacian.
Riemannian starshape and capacitary problems / Ishige, Kazuhiro; Salani, Paolo; Takatsu, Asuka. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - ELETTRONICO. - 85:(2025), pp. 104368.0-104368.0. [10.1016/j.nonrwa.2025.104368]
Riemannian starshape and capacitary problems
Ishige, Kazuhiro;Salani, Paolo
;Takatsu, Asuka
2025
Abstract
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open interval and the unit sphere. We also extend the result by replacing the Laplacian with the q-Laplacian.
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