Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds

Name: Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds
Availability: OutOfStock
ISBN: 9780821808375

ISBN-10: 0821808370

ISBN-13: 9780821808375

Edition: N/A

Authors: Jozef Dodziuk, Jay Jorgensen

List price: $51.00

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In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then…

Book details

List price: $51.00
Publisher: American Mathematical Society
Publication date: 8/30/1998
Binding: Paperback
Pages: 75
Size: 7.25" wide x 10.00" long x 0.25" tall
Weight: 0.330
Language: English



Introduction


Review of hyperbolic geometry


Convergence of heat kernels


Infinite cylinder estimates


Heat kernels and regularized heat traces


Degenerating heat traces


Poisson kernel estimates


Analysis of trace integrals


Convergence of regularized heat traces


Long time asymptotics Spectral zeta functions


Selberg zeta functions Hurwitz-type zeta functions


Asymptotics of spectral measures


Eigenvalue counting problems


Convergence of spectral projections


Bibliography