Geometry of Reinhardt domains of finite type in \(\mathbb{C}^2\)
The author studies the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric near boundary points of finite type of pseudoconvex Reinhardt domains in \(\mathbb{C}^2\) by comparing a domain locally to either a Thullen egg domain or a tube domain. On the model domains, explicit computations are feasible. The author deduces that the Bergman curvature is bounded between two negative constants in a neighborhood of a finite-type boundary point of a smoothly bounded pseudoconvex Reinhardt domain in \(\mathbb{C}^2\). It follows that every smooth, bounded, pseudoconvex, Reinhardt domain of finite type in \(\mathbb{C}^2\) admits a complete Kähler metric with holomorphic sectional curvature bounded between two negative constants.
scientific article; zbMATH DE number 1160127
scientific article