A survey on extensions of Riemannian manifolds and Bartnik mass estimates

DOI10.1090/conm/775/15586zbMath1495.53001arXiv1904.05830OpenAlexW3215122055MaRDI QIDQ5085334

Carla Cederbaum, Armando J. Cabrera Pacheco

Publication date: 27 June 2022

Published in: Mexican Mathematicians in the World (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.05830

zbMATH Keywords

asymptotically flatGaussian curvatureBartnik mass

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (3)

ADM mass in warp drive spacetimes ⋮ Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass ⋮ A note about isotopy and concordance of positive scalar curvature metrics on compact manifolds with boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Bartnik's mass and Hamilton's modified Ricci flow
• Deforming three-manifolds with positive scalar curvature
• Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Smoothing the Bartnik boundary conditions and other results on Bartnik's quasi-local mass
• Quasi-spherical metrics and prescribed scalar curvature
• Flow of nonconvex hypersurfaces into spheres
• On the Riemannian Penrose inequality in dimensions less than eight
• The Cauchy problem in general relativity.
• On a localized Riemannian Penrose inequality
• On the invariant mass conjecture in 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.
• The mass of asymptotically hyperbolic manifolds.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Asymptotically hyperbolic extensions and an analogue of the Bartnik mass
• Exotic hyperbolic gluings
• The Bartnik-Bray outer mass of small metric spheres in time-symmetric 3-slices
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• The mass of asymptotically hyperbolic Riemannian manifolds.
• Quasiconvex foliations and asymptotically flat metrics of non-negative scalar curvature
• Generic regularity of homologically area minimizing hypersurfaces in eight dimensional manifolds
• Higher dimensional black hole initial data with prescribed boundary metric
• On Hawking mass and Bartnik mass of CMC surfaces
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Mass rigidity for hyperbolic manifolds
• Capacity, quasi-local mass, and singular fill-ins
• Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions
• On perturbations of the Schwarzschild anti-de Sitter spaces of positive mass
• Penrose type inequalities for asymptotically hyperbolic graphs
• Embeddings, immersions and the Bartnik quasi-local mass conjectures
• Positive scalar curvature with skeleton singularities
• Parabolic constructions of asymptotically flat 3-metrics of prescribed scalar curvature
• Rigidity and positivity of mass for asymptotically hyperbolic manifolds
• Asymptotically flat extensions with charge
• Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity
• Curvature, Sphere Theorems, and the Ricci flow
• Manifolds with 1/4-pinched curvature are space forms
• Coordinate Invariance and Energy Expressions in General Relativity
• On the Bartnik mass of apparent horizons
• Present status of the Penrose inequality
• The mass of an asymptotically flat manifold
• Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity
• On the connectedness of the space of initial data for the Einstein equations
• On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds
• On compact 3-manifolds with nonnegative scalar curvature with a CMC boundary component
• On the Penrose inequality for charged black holes
• Bartnik mass via vacuum extensions
• On a Penrose-Like Inequality in Dimensions Less than Eight
• Asymptotically flat extensions of CMC Bartnik data
• General Relativity

This page was built for publication: A survey on extensions of Riemannian manifolds and Bartnik mass estimates