\(A_{\infty}\)-weights and compactness of conformal metrics under \(L^{n/2}\) curvature bounds

DOI10.2140/apde.2021.14.2163OpenAlexW4200482944MaRDI QIDQ2063048

Gilles Carron, Samuel Tapie, Clara L. Aldana

Publication date: 10 January 2022

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.05387

zbMATH Keywords

Muckenhoupt weightsYamabe equationcompactness of conformal metrics

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Conformal structures on manifolds (53C18)

Related Items (9)

Sobolev spaces and \(\nabla\)-differential operators on manifolds. I: Basic properties and weighted spaces ⋮ W1,p-metrics and conformal metrics with Ln/2-bounded scalar curvature ⋮ Bubble tree convergence for conformal metrics with \(\int_M | R |^{\frac{n}{2}}\, d V_g\) bounds ⋮ Ricci flow of \(W^{2, 2}\)-metrics in four dimensions ⋮ Sobolev inequalities and convergence for Riemannian metrics and distance functions ⋮ From \(L^p\) bounds to Gromov-Hausdorff convergence of Riemannian manifolds ⋮ Convergence of the Yamabe flow on singular spaces with positive Yamabe constant ⋮ Manifolds for which Huber's theorem holds ⋮ A rigidity result for metric measure spaces with Euclidean heat kernel

Cites Work

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• Strong \(A_\infty\)-weights are \(A_\infty\)-weights on metric spaces
• \(Q\)-curvature and Poincaré metrics
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Strong \(A_{\infty}\)-weights and scaling invariant Besov capacities
• Problèmes isoperimetriques et espaces de Sobolev
• Compactness of conformal metrics with integral bounds on curvature
• Lack of compactness in conformal metrics with \(L^{d/2}\) curvature
• Yamabe metrics of positive scalar curvature and conformally flat manifolds
• Global existence and convergence for a higher order flow in conformal geometry
• The Huber theorem for non-compact conformally flat manifolds
• Stability results for Harnack inequalities.
• Best constants in the Sobolev imbedding theorem
• Geometric inequalities for manifolds with Ricci curvature in the Kato class
• The isoperimetric inequality and \(Q\)-curvature
• Regularity of conformal metrics with large first eigenvalue
• Logarithmic potentials, quasiconformal flows, and \(Q\)-curvature
• Volume of spheres in doubling metric measured spaces and in groups of polynomial growth
• Liouville theorems for harmonic sections and applications

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