A note on complex-hyperbolic Kleinian groups

Abstract

Let $\Gamma$ be a discrete group of isometries acting on the complex hyperbolic $n$-space ${\mathbb{H}}_{\mathbb{C}}^n$. In this note, we prove that if $\Gamma$ is convex-cocompact, torsion-free, and the critical exponent $\delta (\Gamma )$ is strictly lesser than $2$, then the complex manifold ${\mathbb{H}}_{\mathbb{C}}^n/\Gamma$ is Stein. We also discuss several related conjectures.

Minor revision. To appear in Arnold Math. J

References in corpus (1)

• Lectures on complex hyperbolic Kleinian groups

Cited by in corpus (1)

• On quotients of bounded homogeneous domains by unipotent discrete groups