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The Levi problem for j-metric balls of a proper pseudoconvex domain in Cn

Khedhiri Hedi

Bulletin of the Polish Academy of Sciences. Mathematics

2022

Vol. 70, no. 2

115--131

Let Ωj(a,r) be an a-centered j-metric ball of a proper pseudoconvex domain Ω in Cn, with radius r>0. In this paper, we discuss whether Ωj(a,r) can be pseudoconvex and so can be holomorphically convex and vice versa. We study three principal cases of the domain Ω and we provide in each case optimal conditions on a and r for which the original Levi problem can be solved in Ωj(a,r). As an application, we show that Kiselman’s minimum principle can hold in the j-metric setting.

Spirallike mappings on bounded balanced pseudoconvex domain in Cn

Hamada H., Kohr G.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

9-21

In this paper we will give some conditions of spirallikeness for holomorphic mappings defined on bounded balanced pseudoconvex domains in Cn with C1 plurisubharmonic defining functions.