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Deformations of Stein structures and extensions of holomorphic mappings

Franc Forstneric·Marko Slapar
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Abstract

Let X be a Stein manifold, A a closed complex subvariety of X, and f a continuous map from X to a complex manifold Y whose restriction to A is holomorphic. After a homotopic deformation of the Stein structure outside a neighborhood of A in X (and of its smooth structure when X is a Stein surface)we find a holomorphic map from X to Y which agrees with f on A and which is homotopic to f relative to A. The analogous results in the case when the variety A is empty have been obtained in the preprint math.CV/0507212.

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Franc Forstneric, Marko Slapar. 2006-12-01. Deformations of Stein structures and extensions of holomorphic mappings. https://arxiv.org/abs/math/0509419

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