The first eigenvalue of the Laplacian on spheres

DOI10.2748/tmj/1178229837zbMath0393.53024OpenAlexW2048039435MaRDI QIDQ1252530

Shukichi Tanno

Publication date: 1979

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229837

zbMATH Keywords

First Eigenvalue of the LaplacianOdd-Dimensional SphereRiemannian Metric

Mathematics Subject Classification ID

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

Related Items (19)

Index of compact minimal submanifolds of the Berger spheres ⋮ Instability of spheres with deformed Riemannian metrics ⋮ Homogenisation on homogeneous spaces ⋮ Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres ⋮ Coupling, spectral gap and related topics. II ⋮ The Spectrum of a Riemannian Manifold with a Unit Killing Vector Field ⋮ The first eigenvalue of the Laplacian on even dimensional spheres ⋮ Full Laplace spectrum of distance spheres in symmetric spaces of rank one ⋮ Unnamed Item ⋮ Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms ⋮ The first eigenvalue of the Laplacian on tori ⋮ Laplacian eigenvalue functionals and metric deformations on compact manifolds ⋮ Spectre et géométrie conforme des variétés compactes à bord ⋮ Boundedness of the first eigenvalue of the 𝑝-Laplacian ⋮ On the stability of a three-sphere ⋮ The first eigenvalue of a homogeneous CROSS ⋮ The first eigenvalues of finite Riemannian covers ⋮ Variational Problems on Contact Riemannian Manifolds ⋮ The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics

Cites Work

• On the least positive eigenvalue of the Laplacian for compact group manifolds
• The topology of contact Riemannian manifolds
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
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• Unnamed Item

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