Displaying similar documents to “On invariant domains in certain complex homogeneous spaces”

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.

Failure of averaging on multiply connected domains

David E. Barrett (1990)

Annales de l'institut Fourier

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We show that for every open Riemann surface X with non-abelian fundamental group there is a multiple-valued function f on X such that the fiberwise convex hull of the graph of f fails to contain the graph of a single-valued holomorphic function on X .

Holomorphic submersions from Stein manifolds

Franc Forstnerič (2004)

Annales de l’institut Fourier

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We establish the homotopy classification of holomorphic submersions from Stein manifolds to Complex manifolds satisfying an analytic property introduced in the paper. The result is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.

On compact orbits in singular Kähler spaces

Jörg Winkelmann (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.