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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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