Cartan-Thullen theorem for domains spread over ...-spaces.
Central morphisms and envelopes of holomorphy.
Construction d'enveloppes d'holomorphie par l'méthode de H. Cartan et P.Thullen.
Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group
We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection is finite and proper, then has a right inverse
Cousin-I spaces and domains of holomorphy
We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.
Cross theorem
Let D,G ⊂ ℂ be domains, let A ⊂ D, B ⊂ G be locally regular sets, and let X:= (D×B)∪(A×G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M̂ of the envelope of holomorphy X̂ of X such that any function separately holomorphic on X∖M extends to a holomorphic function on X̂ ∖M̂. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].