Peak curves in weakly pseudoconvex boundaries in \(\mathbb{C}^2\)
Let \(D\) be a weakly pseudoconvex domain with real analytic boundary of finite type in \(\mathbb{C}^2\), and let \({\mathcal O}(\overline D)\) be the algebra of holomorphic functions in a neighborhood of \(D\). In this paper a necessary and a sufficient condition are given in order to provide the existence of real analytic curves passing through a point \(p\in\partial D\), which are local peak sets for \({\mathcal O}(\overline D)\). Also the authors explicitly exhibit domains \(D\subset\mathbb{C}^2\) with real analytic boundary and a point \(p\in \partial D\) which is a local peak point for \({\mathcal O}(\overline D)\); yet there are no real analytic curves through \(p\) that are local peak sets for \({\mathcal O}(\overline D)\).
scientific article; zbMATH DE number 1192501
scientific article