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

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- by Jozef Dodziuk and Jeffrey McGowan PDF
- Trans. Amer. Math. Soc.
**347**(1995), 1981-1995 Request permission

## Abstract:

We consider a sequence $({M_n})_{n = 1}^\infty$ of compact hyperbolic manifolds converging to a complete hyperbolic manifold ${M_0}$ with cusps. The Laplace operator acting on the space of ${L^2}$ differential forms on ${M_0}$ has continuous spectrum filling the half-line $[0,\infty )$. One expects therefore that the spectra of this operator on ${M_n}$ 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.## References

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## Additional Information

- © Copyright 1995 American Mathematical Society
- 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