Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian \(3\)-manifolds. (English) Zbl 1491.53069

Chodosh, Otis; Eichmair, Michael

Duke Math. J. 171, No. 1, 1-31 (2022).

Let \((M,g)\) be a connected, complete Riemannian \(3\)-manifold, \(C^5\)-asymptotic to Schwarzschild, with mass \(m>0\). It is known that the complement of a compact subset of \(M\) admits a foliation by distinguished stable constant mean curvature spheres. The main result of this paper states that if \((M,g)\) is a manifold as before, whose scalar curvature vanishes and with horizon boundary, then every connected, closed, embedded, stable constant mean curvature surface in \((M,g)\), of large enough area, is a leaf of the canonical foliation.

Reviewer: Antonella Nannicini (Firenze)

MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C20	Global Riemannian geometry, including pinching

Keywords:

asymptotically flat; constant mean curvature; Hawking mass; Minkowski inequality; scalar curvature; Schwarzschild

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