Structure of the image of analytic discs attached to totally real submanifolds (Q2752842)

The object of this paper is to study analytic disks attached to totally real submanifolds. More precisely, consider maps \(( w: (D^{2} ,\partial D^{2}) \rightarrow (\mathbb{C}^{n},R) ,)\) where \(R\) is a totally real submanifold, let \(\Delta \) denote the interior of \(D^{2} \) and \(bA\) the image of the boundary under \(w.\) The main results of the paper provides a description of \((\Delta \setminus w^{-1} (bA)).\) The first result says that \(( \Delta \setminus w^{-1} (bA))\) can be decomposed into connected components, each one of which becomes, after filling discrete holes, simply connected. The image can be decomposed into a finite union of simple disks attached to the same totally real submanifold. If in addition \(R\) is real-analytic and \(w\) is holomorphic, \(( \Delta \setminus w^{-1} (bA))\) is connected and \(w\) can be expressed as the composition of a simple disk and a finite Blaschke product. Similar results had been obtained earlier by the same authors. Here they have reformulated some results in a SCV setting in order to make them more attractive to specialists of that field.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].