Collapsing of connected sums and the eigenvalues of the Laplacian

DOI10.1016/S0393-0440(01)00033-XzbMath1034.58027OpenAlexW2094080454MaRDI QIDQ1602413

Junya Takahashi

Publication date: 23 June 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0393-0440(01)00033-x

zbMATH Keywords

eigenvaluesLaplaciangluing

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (7)

Spectrum of hypersurfaces with small extrinsic radius or large \(\lambda_{1}\) in Euclidean spaces ⋮ Nodal sets of Laplace eigenfunctions under small perturbations ⋮ Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian ⋮ $p$-spectrum and collapsing of connected sums ⋮ A spinorial analogue of Aubin's inequality ⋮ Approximating orbifold spectra using collapsing connected sums ⋮ On the contact geometry of nodal sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Sur la multiplicité de la première valeur propre non nulle du Laplacien. (On the multiplicity of the first nonzero eigenvalue of the Laplacian)
• Spectra of manifolds with small handles
• Potential and scattering theory on wildly perturbed domains
• An introduction to partial differential equations
• Spectrum of the Laplacian acting on differential \(p\)-forms, and down breaking handles
• Hodge-Laplace operator on compact manifolds deprived of a finite number of balls.
• Spectre du laplacien et écrasement d'anses
• Convergence de variétés et convergence du spectre du laplacien
• Convergence of Alexandrov spaces and spectrum of Laplacian

This page was built for publication: Collapsing of connected sums and the eigenvalues of the Laplacian