An eigenvalue pinching theorem

DOI10.1007/BF01394058zbMath0505.53018MaRDI QIDQ1836395

Christopher B. Croke

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142934

zbMATH Keywords

diameterpinchingfirst eigenvalue of the Laplacian

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (20)

Gromov’s convergence theorem and its application ⋮ Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Unnamed Item ⋮ Quantitative Obata's theorem ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ Metrics of positive Ricci curvature with large diameter ⋮ Pincement sur le spectre et le volume en courbure de Ricci positive ⋮ Geometric and topological rigidity for compact submanifolds of odd dimension ⋮ Extrinsic radius pinching in space forms of nonnegative sectional curvature ⋮ Extrinsic radius pinching for hypersurfaces of space forms ⋮ Smooth diameter and eigenvalue rigidity in positive Ricci curvature ⋮ Ricci curvature and almost spherical multi-suspension ⋮ Model spaces for sharp isoperimetric inequalities ⋮ Rigidity for positive Ricci curvature via metric measure geometry ⋮ Quantitative estimates for the Bakry-Ledoux isoperimetric inequality ⋮ Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. (On an isoperimetric inequality which generalizes that of Paul Lévy-Gromov) ⋮ 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 ⋮ Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

Cites Work

• 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
• Unnamed Item
• Unnamed Item

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