Survey of Oka theory.

Forstnerič, Franc; Lárusson, Finnur

Displaying similar documents to “Survey of Oka theory.”

Holomorphic submersions from Stein manifolds

Franc Forstnerič (2004)

Annales de l’institut Fourier

Similarity:

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

Similarity:

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 $ℂ^{n} \to Y$ . We prove that a holomorphic map $X_{0} \to Y$ from a closed complex subvariety $X_{0}$ in a Stein manifold $X$ admits a holomorphic extension $X \to Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

Affine simplices in Oka manifolds.

Lárusson, Finnur (2009)

Documenta Mathematica

Similarity:

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

Similarity:

We study the extension problem of holomorphic maps $σ : H \to X$ 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 $X$ .

Holomorphic Maps of Generalized Iwasawa Manifolds.

G. Schumacher, A.T. Huckleberry (1979/80)

Manuscripta mathematica

Similarity:

On holomorphic extension of functions on singular real hypersurfaces in $ℂ^{n}$ .

Neelon, Tejinder S. (2001)

International Journal of Mathematics and Mathematical Sciences

Similarity:

On the $D^{*}$ -extension and the Hartogs extension

Do Duc Thai (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Linear Kierst-Szpilrajn theorems

L. Bernal-González (2005)

Studia Mathematica

Similarity:

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...