1. CMB Online first
 Gilligan, Bruce

Levi's problem for pseudoconvex homogeneous manifolds
Suppose $G$ is a connected complex Lie group and $H$ is a closed
complex subgroup.
Then there exists a closed complex subgroup $J$ of $G$ containing
$H$ such that
the fibration $\pi:G/H \to G/J$ is the holomorphic reduction
of $G/H$, i.e., $G/J$ is holomorphically
separable and ${\mathcal O}(G/H) \cong \pi^*{\mathcal O}(G/J)$.
In this paper we prove that if $G/H$ is pseudoconvex, i.e.,
if
$G/H$ admits a continuous plurisubharmonic exhaustion function,
then $G/J$ is Stein and $J/H$ has no nonconstant holomorphic
functions.
Keywords:complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilator Categories:32M10, 32U10, 32A10, 32Q28 

2. CMB 2016 (vol 59 pp. 346)
 Krantz, Steven

On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains
We study and generalize a classical theorem of L. Bers that classifies
domains up to biholomorphic equivalence in terms of the algebras
of
holomorphic functions on those domains. Then we develop applications
of these results to the study of domains with noncompact automorphism
group.
Keywords:Bers's theorem, algebras of holomorphic functions, noncompact automorphism group, biholomorphic equivalence Categories:32A38, 30H50, 32A10, 32M99 

3. CMB 2009 (vol 52 pp. 84)
4. CMB 2000 (vol 43 pp. 294)