Treffer: Applications of subordination chains to starlike mappings in ℂn: Applications of subordination chains to starlike mappings in \(\mathbb{C}^ n\)

We use the work of Pfaltzgraff on subordination chains in \(\mathbb{C}^ n\) to recover a growth theorem for starlike mappings of the unit ball established recently by Barnard, FitzGerald and Gong. The growth theorem in one complex variable is a classical result and holds true for the full class of normalized univalent maps of the unit disc. This is no longer the case if \(n > 1\) whether one works in the unit ball or the polydisc. We also introduce a class of strongly starlike maps for which we construct, aided by the aforementioned technique, an explicit quasiconformal extension to \(\mathbb{C}^ n\). Several examples are discussed at the end.