Metrics of positive Ricci curvature with large diameter

DOI10.1007/BF02568774zbMath0711.53036WikidataQ125840490 ScholiaQ125840490MaRDI QIDQ923388

Michael T. Anderson

Publication date: 1990

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155537

zbMATH Keywords

Ricci curvaturediameterLaplacianexamplesfirst eigenvalues

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)

Related Items (20)

Manifolds tightly covered by two metric balls ⋮ Aspects of global Riemannian geometry ⋮ An excess sphere theorem ⋮ A diameter sphere theorem for manifolds of positive Ricci curvature ⋮ On radius, systole, and positive Ricci curvature ⋮ A note on Andrews inequalities ⋮ Pincement sur le spectre et le volume en courbure de Ricci positive ⋮ Small excess and Ricci curvature ⋮ Sphere theorems for RCD and stratified spaces ⋮ Smooth diameter and eigenvalue rigidity in positive Ricci curvature ⋮ Ricci curvature and almost spherical multi-suspension ⋮ On Riemannian manifolds with \(\epsilon\)-maximal diameter and bounded curvature ⋮ Manifolds of Positive Ricci Curvature with Almost Maximal Volume ⋮ Stability of the Faber-Krahn inequality in positive Ricci curvature. ⋮ Closed manifolds with small excess. ⋮ A Pinching Theorem for Homotopy Spheres ⋮ Cones over metric measure spaces and the maximal diameter theorem ⋮ A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture ⋮ First eigenvalue pinching for euclidean hypersurfaces via \(k\)-th mean curvatures ⋮ Differentiable sphere theorems for Ricci curvature

Cites Work

• Unnamed Item
• Diameter, volume, and topology for positive Ricci curvature
• Short geodesics and gravitational instantons
• Eigenvalue comparison theorems and its geometric applications
• An eigenvalue pinching theorem
• The relation between the Laplacian and the diameter for manifolds of non- negative curvature
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• On Complete Manifolds With Nonnegative Ricci Curvature
• A Sphere Theorem for Manifolds of Positive Ricci Curvature
• Riemannian spaces having their curvature bounded below by a positive number

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