2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136131Let 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. LettComplex VariablesGeometric Topology32H02, 32Q28,32Q30,32Q55,32Q60,32T15,57R17text