SPECTRAL ASYMPTOTICS ON DEGENERATING HYPERBOLIC 3-MANIFOLDS by Jozef Dodziuk, Jay Jorgensen ( 9780821808375 )

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Title:

SPECTRAL ASYMPTOTICS ON DEGENERATING HYPERBOLIC 3-MANIFOLDS

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Format:

Paperback

List price:	£47.50
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ISBN 10:

0821808370

ISBN 13:

9780821808375

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

1 January, 1998

Series:

Memoirs of the American Mathematical Society No. 643

Pages:

Description:

Thurston's hyperbolic surgery theorem asserts the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. This book studies asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions.

Synopsis:

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 asserts 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 convergence of tubes in the manifolds of the sequence to cusps of the limiting manifold.In the spectral theory aspect of the work, they prove convergence of heat kernels. They then define a regularized heat trace associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behavior through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behavior of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration.The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behavior of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.

Publication:

Imprint:

American Mathematical Society

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Returnable

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