Relating notions of convergence in geometric analysis

DOI10.1016/j.na.2020.111993zbMath1448.53050arXiv1911.04522OpenAlexW3032897121MaRDI QIDQ2201740

Christina Sormani, Brian M. Allen

Publication date: 17 September 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04522

zbMATH Keywords

Gromov-Hausdorff convergenceintrinsic flat convergenceLipschitz convergence of distancesmetric measure convergencesequences of conformal metrics

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (8)

Conformal tori with almost non-negative scalar curvature ⋮ Intrinsic flat convergence of points and applications to stability of the positive mass theorem ⋮ \(d_p\)-convergence and \(\epsilon\)-regularity theorems for entropy and scalar curvature lower bounds ⋮ Null distance and Gromov-Hausdorff convergence of warped product spacetimes ⋮ Sobolev inequalities and convergence for Riemannian metrics and distance functions ⋮ Kähler tori with almost non-negative scalar curvature ⋮ From \(L^p\) bounds to Gromov-Hausdorff convergence of Riemannian manifolds ⋮ Almost non-negative scalar curvature on Riemannian manifolds conformal to tori

Cites Work

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• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• The Riemannian \(L^{2}\) topology on the manifold of Riemannian metrics
• Convergence and rigidity of manifolds under Ricci curvature bounds
• Weak convergence of currents and cancellation
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Convergence of Riemannian manifolds; Ricci and \(L^{n/2}\)-curvature pinching
• Diffeomorphism finiteness for manifolds with Ricci curvature and \(L^{n/2}\)-norm of curvature bounded
• Riemannian manifolds with small integral norm of curvature
• Compactness of conformal metrics with integral bounds on curvature
• Lack of compactness in conformal metrics with \(L^{d/2}\) curvature
• Ricci curvature and volume convergence
• Relative volume comparison with integral curvature bounds
• On the structure of spaces with Ricci curvature bounded below. I
• Global existence and convergence for a higher order flow in conformal geometry
• Intrinsic flat Arzela-Ascoli theorems
• Orbifold compactness for spaces of Riemannian metrics and applications
• Integral curvature bounds, distance estimates and applications
• Shape of manifolds with positive Ricci curvature
• Contrasting various notions of convergence in geometric analysis
• Sobolev bounds and convergence of Riemannian manifolds
• The isoperimetric inequality and \(Q\)-curvature
• Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded below
• Warped tori with almost non-negative scalar curvature
• Logarithmic potentials, quasiconformal flows, and \(Q\)-curvature
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• How Riemannian Manifolds Converge
• Convergence of riemannian manifolds with integral bounds on curvature. I
• Convergence of riemannian manifolds with integral bounds on curvature. II
• Analysis and geometry on manifolds with integral Ricci curvature bounds. II
• Properties of the Intrinsic Flat Distance
• Conformal invariants and partial differential equations
• Currents in metric spaces

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