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Extending holomorphic mappings from subvarieties in Stein manifolds

Franc Forstneric (2005)

Annales de l’institut Fourier

Suppose that Y is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space n to Y is a uniform limit of entire maps 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.

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

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 are known in...

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