Compactness Criteria for Riemannian Manifolds

DOI10.2307/2043820zbMath0484.53032OpenAlexW4232733277MaRDI QIDQ3943614

Gregory J. Galloway

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/2043820

zbMATH Keywords

Ricci curvatureindex formcompactness conditions

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (14)

On the geometry of metric measure spaces with variable curvature bounds ⋮ Some Ambrose- and Galloway-type theorems via Bakry-Émery and modified Ricci curvatures ⋮ Some Cheeger-Gromov-Taylor type compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures ⋮ On the compactness of hypersurfaces with finite total curvature via mean curvature flow ⋮ Some results on the occurrence of compact minimal submanifolds ⋮ A remark on compact Ricci solitons ⋮ Myers-type theorems and some related oscillation results ⋮ Uniform decay estimates for finite-energy solutions of semi-linear elliptic inequalities and geometric applications ⋮ Integral curvature bounds and bounded diameter with Bakry-Emery Ricci tensor ⋮ Some compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures with negative \(m\) ⋮ Myers' type theorem for integral Bakry-Émery Ricci tensor bounds ⋮ On some aspects of oscillation theory and geometry ⋮ A generalization of the Cheeger-Gromoll splitting theorem ⋮ The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds

Cites Work

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• A theorem of Myers
• On Ricci curvature and geodesics
• On complete open manifolds of positive curvature
• Konvexe Flächen mit langsam abnehmender Krümmung
• Riemannian manifolds with positive mean curvature
• The behaviour of solutions of a linear differential equation of second order
• Oscillation Criteria for Second-Order Linear Differential Equations
• Energy density and spatial curvature in general relativity
• Non-Oscillation Theorems
• A criterion of oscillatory stability

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