On compact 3-manifolds with nonnegative scalar curvature with a CMC boundary component

DOI10.1090/tran/7500zbMath1392.53055arXiv1610.07513OpenAlexW2963544680WikidataQ125891807 ScholiaQ125891807MaRDI QIDQ4642528

Naqing Xie, Pengzi Miao

Publication date: 23 May 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.07513

zbMATH Keywords

scalar curvatureCMC surfacesRiemannian Penrose inequality

Mathematics Subject Classification ID

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

Related Items

The general relativistic constraint equations, Asymptotically hyperbolic extensions and an analogue of the Bartnik mass, A survey on extensions of Riemannian manifolds and Bartnik mass estimates, NNSC-cobordism of Bartnik data in high dimensions, On the NNSC fill-ins and asymptotically flat extension, 4-Dimensional manifolds with nonnegative scalar curvature and CMC boundary, Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bartnik's mass and Hamilton's modified Ricci flow
• Foliations by stable spheres with constant mean curvature for isolated systems with general asymptotics
• Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry
• The Ricci flow on the 2-sphere
• On a localized Riemannian Penrose inequality
• On the proof of the positive mass conjecture in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
• Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
• Foliations of asymptotically flat 3-manifolds by 2-surfaces of prescribed mean curvature
• Coordinate Invariance and Energy Expressions in General Relativity
• On the Bartnik mass of apparent horizons
• Foliation by Constant Mean Curvature Spheres on Asymptotically Flat Manifolds
• The Weyl and Minkowski problems in differential geometry in the large