Runge approximation on convex sets implies the Oka property


We prove that the classical Oka property of a complex manifold $Y\!$, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to $Y\!$, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to $Y$.


Franc Forstnerič

Institute of Mathematics, Physics and Mechanics, University of Ljubljani, SI-1000 Ljubljana, Slovenia