Area-minimizing surfaces in asymptotically flat three-manifolds

Abstract

We show that an asymptotically flat Riemannian three-manifold with non-negative scalar curvature is isometric to flat ${\mathbb{R}}^3$ if it admits an unbounded area-minimizing surface. This answers a question of R. Schoen.

All comments welcome!

Cited by in corpus (2)

• Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian $3$-manifolds
• Rigidity of marginally outer trapped 2-spheres