Totally real discs in non-pseudoconvex boundaries
Let \(D\) be a relatively compact domain in \(\mathbb C^2\) with smooth connected boundary \(\partial D\). B. Jöricke discovered the remarkable phenomenon that any compact subset of a totally real disc embedded in a strictly pseudoconvex boundary is removable for CR functions. The main result of the paper shows that this holds true without any assumption on pseudoconvexity. Precisely, let \(S\subset\partial D\) be a smoothly embedded totally real disc. Then any compact subset \(K\subset S\) is removable for CR functions, i.e. any continuous CR function \(f\) on \(\partial D\setminus K\) admits a holomorphic extension \(F\in\mathcal O(D)\cap C(D\cup(\partial D\setminus K))\). This result reflects special properties of complex dimension 2.
scientific article; zbMATH DE number 2057367
scientific article