Embeddings, immersions and the Bartnik quasi-local mass conjectures

DOI10.1007/s00023-019-00786-3zbMath1416.83027arXiv1611.08755OpenAlexW3100388663WikidataQ123013294 ScholiaQ123013294MaRDI QIDQ2414924

Jeffrey L. Jauregui, Michael T. Anderson

Publication date: 17 May 2019

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.08755

zbMATH Keywords

embeddingsimmersionsADM massBartnik quasi-local mass

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Gravitational energy and conservation laws; groups of motions (83C40) Applications of PDEs on manifolds (58J90) Global Riemannian geometry, including pinching (53C20) Exact solutions to problems in general relativity and gravitational theory (83C15)

Related Items (10)

The general relativistic constraint equations ⋮ New asymptotically flat static vacuum metrics with near Euclidean boundary data ⋮ Scalar curvature deformation and mass rigidity for ALH manifolds with boundary ⋮ A survey on extensions of Riemannian manifolds and Bartnik mass estimates ⋮ Static potentials and area minimizing hypersurfaces ⋮ The Bartnik-Bray outer mass of small metric spheres in time-symmetric 3-slices ⋮ A quasi-local Penrose inequality for the quasi-local energy with static references ⋮ Bartnik mass via vacuum extensions ⋮ Lower semicontinuity of ADM mass under intrinsic flat convergence ⋮ The Hilbert manifold of asymptotically flat metric extensions

Cites Work

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• A note on mass-minimising extensions
• Bartnik's mass and Hamilton's modified Ricci flow
• Static potentials on asymptotically flat manifolds
• Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
• Quasi-local energy-momentum and angular momentum in general relativity
• Manifold structures for sets of solutions of the general relativistic constraint equations
• Smoothing the Bartnik boundary conditions and other results on Bartnik's quasi-local mass
• Quasi-spherical metrics and prescribed scalar curvature
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Phase space for the Einstein equations
• On boundary value problems for Einstein metrics
• Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
• Role of surface integrals in the Hamiltonian formulation of general relativity
• 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.
• Elliptic partial differential equations of second order
• Spatial metrics which are static in many ways
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Variational and rigidity properties of static potentials
• On the lower semicontinuity of the ADM mass
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time
• Quasiconvex foliations and asymptotically flat metrics of non-negative scalar curvature
• Fill-ins of nonnegative scalar curvature, static metrics, and quasi-local mass
• The phase space for the Einstein-Yang-Mills equations and the first law of black hole thermodynamics
• Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions
• Lower semicontinuity of mass under \(C^0\) convergence and Huisken's isoperimetric mass
• Parabolic constructions of asymptotically flat 3-metrics of prescribed scalar curvature
• Effective versions of the positive mass theorem
• Criteria for positive Green's functions
• On the Bartnik extension problem for the static vacuum Einstein equations
• On the Bartnik mass of apparent horizons
• The mass of an asymptotically flat manifold
• The Boundary Harnack Principle for Non-Divergence form Elliptic Operators
• Static potentials and area minimizing hypersurfaces
• Elliptic equations, principal eigenvalue and dependence on the domain
• Killing vectors in asymptotically flat space–times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• A remark on boundary effects in static vacuum initial data sets
• On the Bartnik conjecture for the static vacuum Einstein equations
• The Weyl and Minkowski problems in differential geometry in the large
• On the structure of solutions to the static vacuum Einstein equations
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

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