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

Differential Geometry 2021-12-06 v1

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.

Keywords

Cite

@article{arxiv.1703.09557,
  title  = {On far-outlying CMC spheres in asymptotically flat Riemannian $3$-manifolds},
  author = {Otis Chodosh and Michael Eichmair},
  journal= {arXiv preprint arXiv:1703.09557},
  year   = {2021}
}

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