Geometric inequalities for electrostatic systems with boundary
Differential Geometry
2026-01-16 v3
Abstract
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous results in the literature. Moreover, we prove sharp boundary estimates and isoperimetric-type inequalities for electrostatic manifolds, as well as volume and boundary inequalities involving the Brown-York and Hawking masses.
Cite
@article{arxiv.2508.10258,
title = {Geometric inequalities for electrostatic systems with boundary},
author = {Allan Freitas and Benedito Leandro and Ernani Ribeiro and Guilherme Sabo},
journal= {arXiv preprint arXiv:2508.10258},
year = {2026}
}
Comments
To appear in Classical and Quantum Gravity