# Separation of sets by Fatou-Bieberbach domains and application to holomorphic mappings

##
Franc Forstnerič

created by risa on 03 Jun 2015

9 jun 2015
-- 16:00

Aula D'Antoni, Dip. Matematica, Università "Tor Vergata", Roma

**Abstract.**

The Andersen-Lempert theory of holomorphic automorphisms of complex
Euclidean spaces $\mathbb{C}^n$ in intimately related to various mapping problems
which are usually classified under the term “modern Oka theory”. In this
talk I will discuss some recent results on the problem of separating a
pair of compact disjoint sets in $\mathbb{C}^n$ by a Fatou-Bieberbach domain, and I
will show how these can be used in the construction of holomorphic
mappings from Stein manifolds of dimension $<n$ to the complement of
certain types of sets in $\mathbb{C}^n$.

** F. Forstneric, T. Ritter: Oka properties of ball complements. Math. Z. 277 (2014) 325-338
** F. Forstneric, E.F. Wold: Fatou-Bieberbach domains in $\mathbb{C}^n \setminus \mathbb{R}^k$. Ark. Mat., in press.