Continuity of relative hyperbolic spectral theory through metric degeneration

DOI10.1215/S0012-7094-96-08402-1zbMath0872.58062OpenAlexW1495379271MaRDI QIDQ1922419

Rolf E. Lundelius, Jay A. Jorgenson

Publication date: 19 October 1997

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08402-1

zbMATH Keywords

Riemann surfaceshyperbolic metricdeterminant of the Laplacianspectral zeta functionsPolyakov formulae

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Determinants and determinant bundles, analytic torsion (58J52) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

The Burghelea-Friedlander-Kappeler–gluing formula for zeta-determinants on a warped product manifold and a product manifold ⋮ Bounds on Faltings's delta function through covers ⋮ Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume ⋮ On the asymptotic behavior of counting functions associated to degenerating hyperbolic Riemann surfaces ⋮ The determinant of the Lax-Phillips scattering operator ⋮ Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula ⋮ Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow ⋮ Precise constants in bosonization formulas on Riemann surfaces. I ⋮ Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps

Cites Work

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• Kernel functions, analytic torsion, and moduli spaces
• Regular 𝑏-groups, degenerating Riemann surfaces, and spectral theory
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

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