7 problems

Let $D$ be a worm domain whose $\overline\partial$-Neumann problem is not globally hypoelliptic. Let $A$ be its boundary annulus, let $V\subset\mathbb C^2$ be an arbitrarily small…

Let $\Omega\subset\mathbb{C}^n$ be a bounded strictly pseudoconvex domain with $C^\infty$ boundary, and let $\omega_B$ denote its Bergman metric. Cheng's conjecture. If $\omega_B$…

Let $\Omega$ be a bounded domain that is not a product domain. A domain is homogeneous if its automorphism group acts transitively, meaning that for any $x,y e \Omega$ there is a…

Let $\widetilde{\Omega} \subset \mathbb{C}^n \times \Delta$ be a pseudoconvex domain. For each $t \in \Delta$, define the fiber … Fix $w\in\mathbb{C}^n$, and assume that every…

Let $\Omega$ be a bounded pseudoconvex domain with $C^\infty$ boundary, and let $\mathcal{L}(\Omega)$ denote the limit set of its automorphism group. A point…

Let $D\subset\mathbb{C}^n$ be a bounded pseudoconvex domain with $C^\infty$ boundary. A domain $D$ is $c$-complete when its Carathéodory pseudodistance $c_D$ is a complete metric.…

Let $\mathcal O_n$ be the ring of germs of holomorphic functions at the origin in $\mathbb C^n$, and let $I$ be the ideal generated by $f_1,\dots,f_l\in\mathcal O_n$, where…