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 $\Gamma$.
Publié le : 1996-05-14
Classification:
11F72,
11Y35,
35P99,
58G25,
65N25
@article{1047591148,
author = {Grunewald, Fritz and Huntebrinker, Wolfgang},
title = {A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp},
journal = {Experiment. Math.},
volume = {5},
number = {4},
year = {1996},
pages = { 57-80},
language = {en},
url = {http://dml.mathdoc.fr/item/1047591148}
}
Grunewald, Fritz; Huntebrinker, Wolfgang. A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp. Experiment. Math., Tome 5 (1996) no. 4, pp. 57-80. http://gdmltest.u-ga.fr/item/1047591148/