Asymptotics of the spectrum of the Laplace operator on Riemannian sol-manifolds in the adiabatic limit

DOI10.1007/s11202-010-0038-zzbMath1213.58019OpenAlexW2064749858WikidataQ115380885 ScholiaQ115380885MaRDI QIDQ606037

Andrey A. Yakovlev

Publication date: 15 November 2010

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

Full work available at URL: https://doi.org/10.1007/s11202-010-0038-z

zbMATH Keywords

spectrumLaplacianadiabatic limitMathieu operatorSol-geometry

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Perturbation theory of linear operators (47A55) Foliations in differential topology; geometric theory (57R30) Perturbations of PDEs on manifolds; asymptotics (58J37)

Cites Work

• Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
• Adiabatic limits on Riemannian sol-manifolds
• Spectra of Sol-manifolds: Arithmetic and quantum monodromy
• The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration
• Global gravitational anomalies
• The spectrum of the Laplacian on Riemannian Heisenberg manifolds
• \(\eta\)-invariants, the adiabatic approximation and conical singularities
• The analysis of elliptic families. II: Dirac operators, êta invariants, and the holonomy theorem
• Local index theory and higher analytic torsion
• Adiabatic limits and spectral geometry of foliations
• Integrable geodesic flows with positive topological entropy
• Adiabatic limits and spectral sequences for Riemannian foliations
• Spectral sequences and adiabatic limits
• Sur le spectre des fibrés en tore qui s'effondrent. (On the spectrum of collapsing torus bundles.)
• Petites valeurs propres et classe d'Euler des S1-fibrés
• APS boundary conditions, eta invariants and adiabatic limits
• Adiabatic limits on Riemannian Heisenberg manifolds
• η-Invariants and Their Adiabatic Limits
• Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
• Semiclassical Spectral Asymptotics on Foliated Manifolds
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