Oberseminar: Tobias Harz (G.15.25)
We discuss the following two results:
Theorem (Gallagher-Harz-Herbort '16): Let $\Omega \subset \mathbb{C}^n$ be a pseudoconvex domain. If the core $\mathfrak{c}'(\Omega)$ with respect to psh functions with at most weak singularities (i.e. Lelong number 0) is empty, then $\Omega$ admits the Bergman metric.
Theorem (Slodkowski '21): There exists a smoohtly bounded strongly pseudoconvex domain $\Omega \subset \mathbb{C}^2$ such that the core $\mathfrak{c}^0(\Omega)$ with respect to continuous psh functions has nonempty interior. However, $\mathfrak{c}'(\Omega)$ is empty, so $\Omega$ still admits the Bergman metric.
