Deformations of Stein structures and extensions of holomorphic mappings

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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.
To appear in Math. Res. Lett

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Complex Variables, Geometric Topology, 32H02, 32Q28,32Q30,32Q55,32Q60,32T15,57R17

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http://salesiana.dossiersoluciones.com/handle/123456789/136131

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509419
 http://arxiv.org/abs/math/0509419
 Math. Res. Lett. 14 (2007), 343--357

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arXiv