Oberseminar: Thomas Pawlaschyk (G.15.25)
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $M$ if and only if the so-called $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$. For $q=1$ we have the classical pseudoconvexity and pseudoconcavity. This is joint-work with Nikolay Shcherbina.
