Geometric inequalities for electrostatic systems with boundary

TL;DR

This paper explores geometric inequalities in electrostatic systems with boundary on compact manifolds, extending previous results to higher dimensions and establishing sharp boundary and isoperimetric inequalities involving mass concepts.

Contribution

It introduces new geometric properties and sharp inequalities for electrostatic manifolds with boundary in higher dimensions, expanding the theoretical framework.

Findings

Established new geometric properties for electrostatic manifolds

Proved sharp boundary estimates and isoperimetric inequalities

Derived volume and boundary inequalities involving Brown-York and Hawking masses

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.