The Levi problem for -metric balls of a proper pseudoconvex domain in \mathbb C^n
Tom 70 / 2022
Streszczenie
Let \Omega _j(a,r) be an a-centered j-metric ball of a proper pseudoconvex domain \Omega in \mathbb C^n, with radius r \gt 0. In this paper, we discuss whether \Omega _j(a,r) can be pseudoconvex and so can be holomorphically convex and vice versa. We study three principal cases of the domain \Omega and we provide in each case optimal conditions on a and r for which the original Levi problem can be solved in \Omega _j(a,r). As an application, we show that Kiselman’s minimum principle can hold in the j-metric setting.