Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume

DOI10.1215/S0012-7094-93-07109-8zbMath0790.58044MaRDI QIDQ1312806

Rolf E. Lundelius

Publication date: 7 February 1994

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

zbMATH Keywords

heightdeterminantLaplacianhyperbolic surface

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Determinants and determinant bundles, analytic torsion (58J52) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items

The Burghelea-Friedlander-Kappeler–gluing formula for zeta-determinants on a warped product manifold and a product manifold, Asymptotics of relative heat traces and determinants on open surfaces of finite area, Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume, Convergence of the normalized spectral counting function on degenerating hyperbolic Riemann surfaces of finite volume, Continuity of relative hyperbolic spectral theory through metric degeneration, CONVERGENCE OF THE HEAT KERNEL AND THE RESOLVENT KERNEL ON DEGENERATING HYPERBOLIC RIEMANN SURFACES OF FINITE VOLUME, Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula, Surfaces with boundary: their uniformizations, determinants of Laplacians, and isospectrality, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, On the appearance of Eisenstein series through degeneration, On the spectral expansion of hyperbolic Eisenstein series, Spectral geometry and scattering theory for certain complete surfaces of finite volume, On the asymptotics of determinant of Laplacian at the principal boundary of the principal stratum of the moduli space of Abelian differentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces
• Extremals of determinants of Laplacians
• The real analytic theory of Teichmüller space
• The asymptotics of the heat equation for a boundary value problem
• Curvature and the eigenvalues of the Laplacian
• Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula
• Can One Hear the Shape of a Drum?
• Diffusion processes in a small time interval
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds