# Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian three-manifolds

## TL;DR

This paper characterizes large, stable constant mean curvature spheres in asymptotically flat 3-manifolds with zero scalar curvature, extending understanding of geometric structures in such spaces.

## Contribution

It provides an unconditional characterization of large stable CMC spheres in asymptotically Schwarzschild manifolds with zero scalar curvature, a significant advancement in geometric analysis.

## Key findings

- Large stable CMC spheres are uniquely characterized in the specified manifolds.
- The result holds unconditionally, without additional assumptions.
- It advances the understanding of geometric structures in asymptotically flat manifolds.

## Abstract

Let $(M, g)$ be a complete Riemannian $3$-manifold that is asymptotic to Schwarzschild with positive mass and whose scalar curvature vanishes. We \textsl{unconditionally} characterize the large, embedded stable constant mean curvature spheres in $(M, g)$.