Spectrum of the Laplacian on asymptotically Euclidean spaces

DOI10.1307/mmj/1030132362zbMath0963.58010OpenAlexW2010414288WikidataQ124919332 ScholiaQ124919332MaRDI QIDQ1590931

Harold Donnelly

Publication date: 1 January 2001

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1030132362

zbMATH Keywords

spectrumLaplaciancomplete Riemannian manifold

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Second-order elliptic equations (35J15)

Related Items (17)

Growth of the eigensolutions of Laplacians on Riemannian manifolds. II: Positivity of the initial energy ⋮ The spectrum of continuously perturbed operators and the Laplacian on forms ⋮ The spectrum of the Laplacian on forms over flat manifolds ⋮ Perturbation of a warped product metric of an end and the growth property of solutions to eigenvalue equations ⋮ Existence of wave operators with time-dependent modifiers for the Schrödinger equations with long-range potentials on scattering manifolds ⋮ Absence of embedded eigenvalues for Riemannian Laplacians ⋮ Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case ⋮ Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian ⋮ On the spectrum of the Laplacian ⋮ Positive curvature and eigenfunctions of the Laplacian ⋮ The radial curvature of an end that makes eigenvalues vanish in the essential spectrum. I ⋮ On open scattering channels for manifolds with ends ⋮ Spectral theory on manifolds ⋮ On open scattering channels for a branched covering of the Euclidean plane ⋮ Radiation condition bounds on manifolds with ends ⋮ Spectral gaps on complete Riemannian manifolds ⋮ Stationary scattering theory on manifolds

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