On the radius pinching estimate and uniqueness of the CMC foliation in asymptotically flat 3-manifolds

DOI10.1016/j.aim.2015.11.009zbMath1330.53034arXiv1207.0281OpenAlexW2963809252WikidataQ125562263 ScholiaQ125562263MaRDI QIDQ900871

Shiguang Ma

Publication date: 23 December 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.0281

zbMATH Keywords

constant mean curvatureasymptotically flat manifold

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Foliations (differential geometric aspects) (53C12)

Related Items

Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds, Isoperimetry for asymptotically flat 3-manifolds with positive ADM mass

Cites Work

• Large outlying stable constant mean curvature spheres in initial data sets
• Foliations by stable spheres with constant mean curvature for isolated systems with general asymptotics
• Uniqueness of the foliation of constant mean curvature spheres in asymptotically flat 3-manifolds
• Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry
• Optimal rigidity estimates for nearly umbilical surfaces
• Curvature estimates for minimal hypersurfaces
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Existence of surfaces minimizing the Willmore functional
• Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
• Large isoperimetric surfaces in initial data sets
• Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
• Foliations of asymptotically flat 3-manifolds by 2-surfaces of prescribed mean curvature
• A \(C^{0}\) estimate for nearly umbilical surfaces
• On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds
• The mass of an asymptotically flat manifold
• Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds
• On the center of mass of isolated systems with general asymptotics
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ