Quasi-spherical metrics and the static Minkowski inequality

TL;DR

This paper proves that in asymptotically flat static manifolds, the Minkowski inequality's equality case uniquely characterizes slices of Schwarzschild space, deepening understanding of geometric inequalities in general relativity.

Contribution

It establishes the uniqueness of Schwarzschild slices as the only equality cases in the Minkowski inequality for static manifolds.

Findings

Equality in the Minkowski inequality characterizes Schwarzschild slices.

The result applies to asymptotically flat static manifolds.

The paper advances geometric analysis in general relativity.

Abstract

We prove that equality within the Minkowski inequality for asymptotically flat static manifolds is achieved only by slices of Schwarzschild space.