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arXiv · 1703.09557

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

Otis Chodosh·Michael Eichmair
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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.

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Otis Chodosh, Michael Eichmair. 2017-03-28. On far-outlying CMC spheres in asymptotically flat Riemannian $3$-manifolds. https://doi.org/10.1515/crelle-2019-0034

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