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1996 A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp
Fritz Grunewald, Wolfgang Huntebrinker
Experiment. Math. 5(1): 57-80 (1996).

Abstract

Let $\hz_{3}$ be three-dimensional hyperbolic space and $\Gamma$ a group of isometries of $\hz_3$ that acts discontinuously on $\hz_{3}$ and that has a fundamental domain of finite hyperbolic volume. The Laplace operator $\MinusDelta$ of $\hz_{3}$ gives rise to a positive, essentially selfadjoint operator on $L^2(\Gamma \backslash \hz_{3})$. The nature of its discrete spectrum $\dspec (\Gamma)$ is still not well understood if $\Gamma$ is not cocompact.

This paper contains a report on a numerical study of $\dspec (\Gamma)$ for various noncocompact groups $\Gamma$. Particularly interesting are the results for some nonarithmetic groups $\Gamma$.

Citation

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Fritz Grunewald. Wolfgang Huntebrinker. "A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp." Experiment. Math. 5 (1) 57 - 80, 1996.

Information

Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0870.65092
MathSciNet: MR1420720

Subjects:
Primary: 11F72
Secondary: 11Y35 , 35P99 , 58G25 , 65N25

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 1 • 1996
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