Riemannian manifolds with small integral norm of curvature

DOI10.1215/S0012-7094-92-06519-7zbMath0762.53026OpenAlexW2093965348WikidataQ115240169 ScholiaQ115240169MaRDI QIDQ1191880

Deane Yang

Publication date: 27 September 1992

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-92-06519-7

zbMATH Keywords

isoperimetric inequalitiesRicci flowinjectivity radiuscollapsinggeodesic ballsSobolev constant

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items

A Concentration-Collapse Decomposition forL²Flow Singularities ⋮ Sobolev inequalities and convergence for Riemannian metrics and distance functions ⋮ From \(L^p\) bounds to Gromov-Hausdorff convergence of Riemannian manifolds ⋮ Structure theory and convergence in Riemannian geometry ⋮ Ricci curvature integrals, local functionals, and the Ricci flow ⋮ Relating notions of convergence in geometric analysis ⋮ On the stability of \(L^p\)-norms of Riemannian curvature at rank one symmetric spaces ⋮ Curvature and injectivity radius estimates for Einstein 4-manifolds ⋮ Analysis and geometry on manifolds with integral Ricci curvature bounds. II

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Collapsing Riemannian manifolds while keeping their curvature bounded. II
• Convergence and rigidity of manifolds under Ricci curvature bounds
• Volume and bounded cohomology
• Collapsing Riemannian manifolds while keeping their curvature bounded. I
• Lipschitz convergence of Riemannian manifolds
• Convergence of Riemannian manifolds; Ricci and \(L^{n/2}\)-curvature pinching
• Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.
• Some isoperimetric inequalities and eigenvalue estimates
• Convergence of riemannian manifolds with integral bounds on curvature. I
• Convergence of riemannian manifolds with integral bounds on curvature. II
• Finiteness Theorems for Riemannian Manifolds