Abstract
 We investigate the spectrum of the automorphic Laplace-Beltrami operator on discrete quotients of
complex hyperbolic space. This is a joint work with Peter Lax. Let $\Gamma$ be a geometrically  finite,
discrete subgroup of holomorphic isometries of the complex hyperbolic space. We assume  that  the
fundamental domain is noncompact, has finite complex hyperbolic volume. The fundamental  domain
is allowed to have finitely many cusps of maximal rank. Under these assumptions, we prove that the
spectrum of the automorphic Laplace-Beltrami operator consists of the union of a standard point
spectrum and an absolutely continuous part of uniform multiplicity, which is equal to the interval
$(-\infty, -n^{2}/4)$. The uniform multiplicity of the absolutely continuous part of the spectrum
is equal to the number of cusps of maximal rank.