A Green's function proof of the positive mass theorem

DOI10.1007/s00220-024-04941-8arXiv2108.08402MaRDI QIDQ6202455

Francesca Oronzio, Virginia Agostiniani, Lorenzo Mazzieri

Publication date: 26 February 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.08402

Mathematics Subject Classification ID

Partial differential equations on manifolds; differential operators (58Jxx) Global differential geometry (53Cxx) General relativity (83Cxx)

Related Items (1)

New monotonicity for \(p\)-capacitary functions in 3-manifolds with nonnegative scalar curvature

Cites Work

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• Nodal sets for solutions of elliptic equations
• On the mass of static metrics with positive cosmological constant: II.
• Asymptotic behavior for singularities of the mean curvature flow
• Large-sphere and small-sphere limits of the Brown-York mass
• Capacitary functions in convex rings
• On the proof of the positive mass conjecture in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Critical sets of solutions to elliptic equations.
• A new proof of the positive energy theorem.
• Ricci flow on asymptotically Euclidean manifolds
• New monotonicity formulas for Ricci curvature and applications. I
• The energy and the linear momentum of space-times in general relativity
• Spacetime harmonic functions and the mass of 3-dimensional asymptotically flat initial data for the Einstein equations
• Scalar curvature and harmonic maps to \(S^1\)
• The anisotropic \(p\)-capacity and the anisotropic Minkowski inequality
• Minkowski inequalities via nonlinear potential theory
• Harmonic functions and the mass of 3-dimensional asymptotically flat Riemannian manifolds
• Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
• A geometric capacitary inequality for sub-static manifolds with harmonic potentials
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
• Capacity, quasi-local mass, and singular fill-ins
• Monotonicity formulas in potential theory
• On the geometry of the level sets of bounded static potentials
• Ricci curvature and monotonicity for harmonic functions
• On the uniqueness of Schwarzschild-de Sitter spacetime
• On the mass of static metrics with positive cosmological constant: I
• The mass of an asymptotically flat manifold
• ENERGY EXTRACTION*
• ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR
• Positivity of mass for certain spacetimes with horizons
• Monotonicity and its analytic and geometric implications
• Geometric Relativity
• On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds
• Comparison Theorems for 3D Manifolds With Scalar Curvature Bound
• A new proof of the Riemannian Penrose inequality
• Spacetime Harmonic Functions and Applications to Mass

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