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Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...

On a Domain Equivalent to the Bidisk.

John Wermer (1980)

Mathematische Annalen

On $q$ -Runge pairs

Mihnea Colţoiu (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a $4$ -complete open subset $D \subset ℂ^{6}$ (which is an analytic complement in the unit ball) such that the restriction map $H^{3} (ℂ^{6}, ℱ) \to H^{3} (D, ℱ)$ has a dense image for every $ℱ \in C o h (ℂ^{6})$ but the pair $(D, ℂ^{6})$ is not a $4$ -Runge pair.

On the Bernstein-Walsh-Siciak theorem

Rafał Pierzchała (2012)

Studia Mathematica

By the Oka-Weil theorem, each holomorphic function f in a neighbourhood of a compact polynomially convex set $K \subset ℂ^{N}$ can be approximated uniformly on K by complex polynomials. The famous Bernstein-Walsh-Siciak theorem specifies the Oka-Weil result: it states that the distance (in the supremum norm on K) of f to the space of complex polynomials of degree at most n tends to zero not slower than the sequence M(f)ρ(f)ⁿ for some M(f) > 0 and ρ(f) ∈ (0,1). The aim of this note is to deduce the uniform version,...

On the extension of L2 holomorphic functions III: negligible weights.

Takeo Ohsawa (1995)

Mathematische Zeitschrift

On the homology groups of $q$ -complete spaces

Edoardo Ballico, Giorgio Bolondi (1983)

Rendiconti del Seminario Matematico della Università di Padova

On the homology groups of Stein spaces and Runge pairs.

M. Coltoiu, N. Mihalache (1986)

Journal für die reine und angewandte Mathematik

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.

Barnet M. Weinstock (1988)

Mathematische Annalen

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