Negative curvature and embedded eigenvalues

DOI10.1007/BF02570738zbMath0699.53052MaRDI QIDQ913276

Harold Donnelly

Publication date: 1990

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174129

zbMATH Keywords

essential spectrumLaplaciannegative sectional curvaturedecay conditions

Mathematics Subject Classification ID

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

Related Items (13)

The spectrum of the Martin-Morales-Nadirashvili minimal surfaces is discrete ⋮ Absence of eigenvalue at the bottom of the continuous spectrum on asymptotically hyperbolic manifolds ⋮ Growth of the eigensolutions of Laplacians on Riemannian manifolds. II: Positivity of the initial energy ⋮ The spectrum of the Laplacian and volume growth of proper minimal submanifolds ⋮ On the number of bound states of point interactions on hyperbolic manifolds ⋮ Perturbation of a warped product metric of an end and the growth property of solutions to eigenvalue equations ⋮ 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 ⋮ Spectrum Estimates and Applications to Geometry ⋮ Riemannian submersions with discrete spectrum ⋮ The radial curvature of an end that makes eigenvalues vanish in the essential spectrum. I ⋮ On some aspects of oscillation theory and geometry ⋮ Riemannian manifolds whose Laplacians have purely continuous spectrum

Cites Work

• A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
• Noncompact Riemannian manifolds with purely continuous spectrum
• On the essential spectrum of a complete Riemannian manifold
• Eigenvalues embedded in the continuum for negatively curved manifolds
• On the spectrum of the laplacian on complete riemannian manifolds
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