Abstract
We construct Fatou–Bieberbach domains in \(\mathbb{C}^{n}\) 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 \(\mathbb{C}^{n}\setminus\mathbb{R}^{k}\) for 1≤k<n enjoys the basic Oka property with approximation for maps from any Stein manifold of dimension <n.
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Forstnerič, F., Wold, E.F. Fatou–Bieberbach domains in \(\mathbb{C}^{n}\setminus\mathbb{R}^{k}\) . Ark Mat 53, 259–270 (2015). https://doi.org/10.1007/s11512-014-0209-4
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DOI: https://doi.org/10.1007/s11512-014-0209-4