Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ${\u2102}^{n}$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

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 ${\pi}_{1}:V\to \Gamma $ is finite and proper, then ${R}_{V}:O\left(\Gamma \times G\right)\to Im{R}_{V}\subset O\left(V\right)$ has a right inverse

The Banach hyperbolicity and disc-convexity of complex Banach manifolds and their relations are investigated.

We show a relation between the Kobayashi pseudodistance of a holomorphic fiber bundle and the Kobayashi pseudodistance of its base. Moreover, we prove that a holomorphic fiber bundle is taut iff both the fiber and the base are taut.

The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V\subset {\mathbb{P}}_{k\u0305}^{m}$, where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V\subset {\mathbb{P}}_{\u2102}^{m}.$

A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...

We give unicity theorems for meromorphic mappings of ${\u2102}^{m}$ into ℂPⁿ with Fermat moving hypersurfaces.

A necessary and sufficient condition for tautness of locally taut domains in a weakly Brody hyperbolic complex space is given. Moreover, some results of Kobayashi and Gaussier are deduced as corollaries.

We introduce the notion of (n,d)-sets and show several Noguchi-type convergence-extension theorems for (n,d)-sets.

Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.

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