2014/01/31 by Franc Forstnerič, Franc Forstneric, Erlend Fornaess Wold +1 · 4 citations
Mathematics · #Affine transformation #Analytic and geometric function theory #Construct (python library) #Dimension (graph theory) #Domain (mathematical analysis) #Geometry and complex manifolds #Holomorphic and Operator Theory #Manifold (fluid mechanics) #Property (philosophy) #Set (abstract data type) #Stein manifold #Subspace topology #math.CV #msc:32E10 #msc:32E20 #msc:32E30 #msc:32H02
paper · pdf · doi:10.1007/s11512-014-0209-4
published in Arkiv för matematik 53(2), 259-270 (Mittag-Leffler Institute) · To appear in Ark. Mat
arxiv created 2014/11/24 · openalex publication_date 2015/01/27 · arxiv updated 2015/09/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 ℂn∖ℝk for 1≤k< n enjoys the basic Oka property with approximation for maps from any Stein manifold of dimension < n.