Sharp lower bound for the charged Hawking mass in the electrostatic space

TL;DR

This paper establishes precise lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times, providing new insights into geometric inequalities and stability criteria in these settings.

Contribution

It introduces sharp lower bounds for the charged Hawking mass and stability criteria for surfaces in electrostatic space-times, advancing understanding of geometric properties in these contexts.

Findings

Sharp lower bounds for the charged Hawking mass.

Upper bounds on the genus of stable surfaces.

Stability criteria for CMC surfaces in Reissner-Nordstrom deSitter space.

Abstract

We prove sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times in various contexts. An upper bound for the genus of stable surfaces in the electrostatic system is provided. We also study the positivity for the charged Hawking mass of a minimal surface with index one in the electrostatic space-times. A criterion for a CMC surface in the Reissner-Nordstrom deSitter space to be stable is presented.