On far-outlying CMC spheres in asymptotically flat Riemannian $3$-manifolds

Abstract

We extend the Lyapunov-Schmidt analysis of outlying stable CMC spheres in the work of S. Brendle and the second-named author to the "far-off-center" regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable CMC spheres that depend very delicately on the behavior of scalar curvature at infinity.

All comments welcome!

References in corpus (2)

• Effective versions of the positive mass theorem
• Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds

Cited by in corpus (3)

• Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian $3$-manifolds
• The Willmore center of mass of initial data sets
• Adiabatic theory for the area-constrained Willmore flow