A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture

DOI10.5802/aif.1358zbMath0783.53024OpenAlexW2329503035WikidataQ123130706 ScholiaQ123130706MaRDI QIDQ1313325

Said Ilias

Publication date: 13 March 1994

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1993__43_3_843_0

zbMATH Keywords

Ricci curvaturediametersectional curvaturefirst eigenvalueLaplacianpinching condition

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items

Some isolation results for \(f\)-harmonic maps on weighted Riemannian manifolds with boundary, Pinching of the first eigenvalue of the Laplacian and almost-Einstein hypersurfaces of the Euclidean space, Extrinsic radius pinching in space forms of nonnegative sectional curvature, Extrinsic radius pinching for hypersurfaces of space forms, Maximizing mean exit-time of the Brownian motion on Riemannian manifolds, First eigenvalue pinching for euclidean hypersurfaces via \(k\)-th mean curvatures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diameter, volume, and topology for positive Ricci curvature
• Constantes explicites pour les inégalités de Sobolev sur les variétés Riemanniennes compactes
• On manifold of positive Ricci curvature with large diameter
• Metrics of positive Ricci curvature with large diameter
• Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. (On an isoperimetric inequality which generalizes that of Paul Lévy-Gromov)
• Examples of manifolds of positive Ricci curvature
• A topological version of Obata's sphere theorem
• Pinching theorem for the first eigenvalue on positively curved manifolds
• Pinching theorem for the first eigenvalue on positively curved four- manifolds
• Eigenvalue comparison theorems and its geometric applications
• A generalized sphere theorem
• An eigenvalue pinching theorem
• Some decompositions of the space of symmetric tensors on a Riemannian manifolds
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• A Diameter Pinching Sphere Theorem for Positive Ricci Curvature
• Harmonic Mappings of Spheres
• Riemannian spaces having their curvature bounded below by a positive number