The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds

Authors:
Jozef Dodziuk and Jeffrey McGowan

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1981-1995

MSC:
Primary 58G25; Secondary 35P15

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308007-X

MathSciNet review:
1308007

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Abstract: We consider a sequence of compact hyperbolic manifolds converging to a complete hyperbolic manifold with cusps. The Laplace operator acting on the space of differential forms on has continuous spectrum filling the half-line . One expects therefore that the spectra of this operator on accumulate to produce the continuous spectrum of the limiting manifold. We prove that this is the case and obtain a sharp estimate of the rate of accumulation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308007-X

Article copyright:
© Copyright 1995
American Mathematical Society