Đề tài " 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 . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...