Displaying similar documents to “Affine simplices in Oka manifolds.”

Survey of Oka theory.

Forstnerič, Franc, Lárusson, Finnur (2011)

The New York Journal of Mathematics [electronic only]

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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.

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.

Linear Kierst-Szpilrajn theorems

L. Bernal-González (2005)

Studia Mathematica

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We prove the following result which extends in a somewhat "linear" sense a theorem by Kierst and Szpilrajn and which holds on many "natural" spaces of holomorphic functions in the open unit disk 𝔻: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in 𝔻 whose domain of holomorphy is 𝔻 except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full...

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 .