Positivity of quasi-local mass II

DOI10.1090/S0894-0347-05-00497-2zbMath1081.83008arXivmath/0412292OpenAlexW1571962299MaRDI QIDQ5695778

Chiu-Chu Melissa Liu, Shing Tung Yau

Publication date: 6 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0412292

zbMATH Keywords

positive mass theoremboundary valuesendsDirac spinorscalar flat metricRiemannian caseasymptotically flat Lipschitz metricJang's equation with Dirichlet boundary conditionlocal energy conditionpositivity of quasi-local energy

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Gravitational energy and conservation laws; groups of motions (83C40) Spin and Spin({}^c) geometry (53C27) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Isometric embeddings into the Minkowski space and new quasi-local mass ⋮ A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold ⋮ Quasi-local mass via isometric embeddings: a review from a geometric perspective ⋮ The Dirac operator on untrapped surfaces ⋮ Optimal choices of reference for a quasi-local energy ⋮ A localized spacetime Penrose inequality and horizon detection with quasi-local mass ⋮ The dihedral rigidity conjecture for \(n\)-prisms ⋮ Brown–York energy in stationary spacetimes ⋮ On geometric problems related to Brown-York and Liu-Yau quasilocal mass ⋮ The Minkowski formula and the quasi-local mass ⋮ Extension of a theorem of Shi and Tam ⋮ A quasi-local Penrose inequality for the quasi-local energy with static references ⋮ A new quasi-local mass and positivity ⋮ Dirac operators on time flat submanifolds with applications ⋮ Curvature estimates for immersed hypersurfaces in Riemannian manifolds ⋮ Quasi-local energy-momentum and angular momentum in general relativity ⋮ Critical points of Wang-Yau quasi-local energy ⋮ Quasi-local energy for spherically symmetric spacetimes ⋮ Positivity of the Bondi mass in Bondi's radiating spacetimes ⋮ Quasi-local mass and isometric embedding with reference to a static spacetime ⋮ A quasi-local mass for 2-spheres with negative Gauss curvature ⋮ Quasi-local mass at axially symmetric null infinity ⋮ Geometric inequalities for quasi-local masses ⋮ A holographic principle for the existence of imaginary Killing spinors ⋮ A free boundary isometric embedding problem in the unit ball

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-spherical metrics and prescribed scalar curvature
• On Witten's proof of the positive energy theorem
• Proof of the positive mass theorem. II
• A simple derivation of canonical structure and quasi-local Hamiltonians in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• Quasi-local energy-momentum and angular momentum in gr: a review article
• Geometry of three manifolds and existence of black hole due to boundary effect
• Some results on surface theory in the large
• Comment on “Positivity of Quasilocal Mass”
• Positivity of Quasilocal Mass
• Momentum, angular momentum and their quasi-local null surface extensions
• More on Penrose's quasi-local mass
• ENERGY EXTRACTION*
• Collapsing shells and the isoperimetric inequality for black holes
• Quasilocal mass constructions with positive energy
• The gravitational Hamiltonian, action, entropy and surface terms
• New variables, the gravitational action and boosted quasilocal stress - energy - momentum
• Spherical Symmetry and Mass-Energy in General Relativity. I. General Theory
• Eigenvalues of the Dirac operator on manifolds with boundary