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1. CMB 2017 (vol 60 pp. 736)

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 non--constant holomorphic functions. Keywords:complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilatorCategories: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 equivalenceCategories:32A38, 30H50, 32A10, 32M99

3. CMB 2009 (vol 52 pp. 84)

Gauthier, P. M.; Zeron, E. S.
 Hartogs' Theorem on Separate Holomorphicity for Projective Spaces If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic. Keywords:separately holomorphic, projective spaceCategories:32A10, 32D99, 32H99

4. CMB 2000 (vol 43 pp. 294)

Bracci, Filippo
 Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity We identify a class of domains of $\C^n$ in which any two commuting holomorphic self-maps have a common fixed point. Keywords:Holomorphic self-maps, commuting functions, fixed points, Wolff point, Julia's LemmaCategories:32A10, 32A40, 32H15, 32A30
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