Fatou-Bieberbach domains in Cⁿᵏ

الأصل · EN

We construct Fatou-Bieberbach domains in Cⁿ for n>1 which contain a given compact set K and at the same time avoid a totally real affine subspace L of dimension <n, provided that K∪ L is polynomially convex. By using this result, we show that the domain Cⁿᵏ for 1≤ k<n enjoys the Oka property with approximation for maps from any Stein manifold of dimension <n.