2012/07/02 by Shiguang Ma, Ma, Shiguang
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1207.0281
40Pages. A strengthened version of arXiv:1207.0281, "A new result on the uniqueness of the CMC foliation in asymptotically flat manifold". arXiv admin note: text overlap with arXiv:1012.3231
openalex publication_date 2012/07/02 · arxiv created 2014/10/24 · arxiv updated 2014/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the uniqueness problem of the constant mean curvature spheres in asymptotically flat 3-manifolds. We require the metric have the form gij=δij+hij with hij=O4(r-1) and R=O(r-3-τ),τ>0. We do not require the metric to be close to Schwarzschild metric in any sense or to satisfy RT conditions. We prove that, when the mass is not 0, stable CMC spheres that separate a certain compact part from infinity satisfy the radius pinching estimate r1≤ Cr0 , which in many cases is critical to prove the uniqueness of the CMC spheres. As applications of this estimate, we remove the radius conditions of the uniqueness result in [Huang-CMC] and [NERZ-CMC] in some special cases.