# Oka manifolds: From Oka to Stein and back

@inproceedings{Forstneri2012OkaMF, title={Oka manifolds: From Oka to Stein and back}, author={Franc Forstneri{\vc}}, year={2012} }

Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert's classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.
In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 25 CITATIONS

## Interpolation by conformal minimal surfaces and directed holomorphic curves

VIEW 9 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Complete minimal surfaces densely lying in arbitrary domains of $\mathbb{R}^n$

VIEW 11 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Oka complements of countable sets and non-elliptic Oka manifolds

VIEW 1 EXCERPT

CITES BACKGROUND

## Elliptic characterization and localization of Oka manifolds.

VIEW 1 EXCERPT

CITES BACKGROUND

## Holomorphic approximation: the legacy of Weierstrass, Runge, Oka-Weil, and Mergelyan

VIEW 1 EXCERPT

CITES BACKGROUND

## Mergeljan's and Arakeljan's theorems for manifold-valued maps

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 79 REFERENCES

## Mapping cylinders and the Oka principle

VIEW 18 EXCERPTS

HIGHLY INFLUENTIAL

## Espaces fibrés analytiques

VIEW 29 EXCERPTS

HIGHLY INFLUENTIAL

## Orbifolds, special varieties and classification theory

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Orbifolds, special varieties and classification theory: an appendix

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Model structures and the Oka Principle

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2 + 1

VIEW 28 EXCERPTS

HIGHLY INFLUENTIAL

## Oka’s principle for holomorphic sections of elliptic bundles

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Nonsingular mappings of Stein manifolds

VIEW 28 EXCERPTS

HIGHLY INFLUENTIAL

## HOLOMORPHIC MAPS INTO COMPLEX PROJECTIVE SPACE

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL