Compactness of conformal metrics with integral bounds on curvature

DOI10.1215/S0012-7094-93-07212-2zbMath0809.53040OpenAlexW1831630849MaRDI QIDQ1320594

Matthew J. Gursky

Publication date: 28 March 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-93-07212-2

zbMATH Keywords

conformal classcurvature boundvolume bound

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items

Compactness of conformal metrics with integral bounds on Ricci curvature ⋮ Lack of compactness in conformal metrics with \(L^{d/2}\) curvature ⋮ W1,p-metrics and conformal metrics with Ln/2-bounded scalar curvature ⋮ Unnamed Item ⋮ Regularity of conformal metrics with large first eigenvalue ⋮ Compactness of isospectral conformal metrics and isospectral potentials on a 4-manifold ⋮ Bubble tree convergence for conformal metrics with \(\int_M | R |^{\frac{n}{2}}\, d V_g\) bounds ⋮ Long time existence of Yamabe flow on singular spaces with positive Yamabe constant ⋮ Conformal metric sequences with integral-bounded scalar curvature ⋮ Convergence of the Yamabe flow on singular spaces with positive Yamabe constant ⋮ Relating notions of convergence in geometric analysis ⋮ Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds. ⋮ The Yamabe problem on stratified spaces ⋮ The Li-Yau-Hamilton inequality for Yamabe flow on a closed CR 3-manifold ⋮ The Fourth-OrderQ-Curvature Flow on Closed 3-Manifolds ⋮ Three-manifolds with small \(L^2\)-norm of traceless-Ricci curvature pinching ⋮ On isospectral compactness in conformal class for 4-manifolds ⋮ \(A_{\infty}\)-weights and compactness of conformal metrics under \(L^{n/2}\) curvature bounds ⋮ Compactness of pseudo-Hermitian structures with integral bounds on curvature

Cites Work

• Conformal deformation of a Riemannian metric to constant scalar curvature
• Compact isospectral sets of surfaces
• Extremals of determinants of Laplacians
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Isospectral sets of conformally equivalent metrics
• Compactness of isospectral conformal metrics on \(S^ 3\)
• Curvature and the eigenvalues of the Laplacian
• Isospectral Conformal Metrics on 3-Manifolds
• The Yamabe problem
• L p pinching and compactness theorems for compact Riemannian manifolds
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