Lower semicontinuity of ADM mass under intrinsic flat convergence

DOI10.1007/s00526-021-02048-9zbMath1487.53086arXiv1903.00916OpenAlexW3191899253WikidataQ115386499 ScholiaQ115386499MaRDI QIDQ2048912

Jeffrey L. Jauregui, Dan A. Lee

Publication date: 24 August 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00916

zbMATH Keywords

integral currentsisoperimetric massCheeger-Gromov convergenceinteger rectifiableintrinsic flat volume convergencespace of asymptotically flat 3-manifolds

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) General relativity (83C99) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (2)

Global hyperbolicity through the eyes of the null distance ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• The pointed flat compactness theorem, for locally integral currents
• Smoothing the Bartnik boundary conditions and other results on Bartnik's quasi-local mass
• Semicontinuity of eigenvalues under intrinsic flat convergence
• Flat convergence for integral currents in metric spaces
• Large-sphere and small-sphere limits of the Brown-York mass
• 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.
• On the lower semicontinuity of the ADM mass
• Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry
• The nonlinear stability of rotationally symmetric spaces with low regularity
• Lower semicontinuity of the ADM mass in dimensions two through seven
• Lower semicontinuity of mass under \(C^0\) convergence and Huisken's isoperimetric mass
• Length structures on manifolds with continuous Riemannian metrics
• Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Embeddings, immersions and the Bartnik quasi-local mass conjectures
• Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
• Normal and integral currents
• The parametric \(h\)-principle for minimal surfaces in \(\mathbb{R}^n\) and null curves in \(\mathbb{C}^n\)
• Coordinate Invariance and Energy Expressions in General Relativity
• The mass of an asymptotically flat manifold
• Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds
• Scalar Curvature and Intrinsic Flat Convergence
• Geometrostatic Manifolds of Small ADM Mass
• Heat semigroup and functions of bounded variation on Riemannian manifolds
• Currents in metric spaces

This page was built for publication: Lower semicontinuity of ADM mass under intrinsic flat convergence