Displaying similar documents to “Holomorphic submersions from Stein manifolds”

Extending holomorphic mappings from subvarieties in Stein manifolds

Franc Forstneric (2005)

Annales de l’institut Fourier

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Suppose that Y is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ℂ n to Y is a uniform limit of entire maps ℂ n → Y . We prove that a holomorphic map X 0 → Y from a closed complex subvariety X 0 in a Stein manifold X admits a holomorphic extension X → Y provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

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We study the extension problem of holomorphic maps σ : H → X of a Hartogs domain H with values in a complex manifold X . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain Ω σ of extension for σ over Δ is contained in a subdomain of Δ . For such manifolds, we define, in this paper, an invariant Hex n ( X ) using the Hausdorff dimensions of the singular sets of σ ’s and study its properties to deduce informations on the complex structure of X .

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

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Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...