Riemannian starshape and capacitary problems
Analysis of PDEs
2024-08-30 v1 Differential Geometry
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 -Laplacian.
Cite
@article{arxiv.2408.16435,
title = {Riemannian starshape and capacitary problems},
author = {Kazuhiro Ishige and Paolo Salani and Asuka Takatsu},
journal= {arXiv preprint arXiv:2408.16435},
year = {2024}
}
Comments
16 pages. Comments welcome!