Arkiv för Matematik

Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration

Miran Černe

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LetX(-ϱBm×Cn be a compact set over the unit sphere ϱBm such that for each z∈ϱBm the fiber Xz={ω∈Cn;(z, ω)∈X} is the closure of a completely circled pseudoconvex domain in Cn. The polynomial hull $\hat X$ of X is described in terms of the Perron-Bremermann function for the homogeneous defining function of X. Moreover, for each point (z0, w0)∈Int $\hat X$ there exists a smooth up to the boundary analytic disc F:Δ→Bm×Cn with the boundary in X such that F(0)=(z0, w0).


This work was supported in part by a grant from the Ministry of Science of the Republic of Slovenia.

Article information

Ark. Mat., Volume 40, Number 1 (2002), 27-45.

Received: 25 April 2000
Revised: 22 June 2001
First available in Project Euclid: 31 January 2017

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2002 © Institut Mittag-Leffler


Černe, Miran. Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration. Ark. Mat. 40 (2002), no. 1, 27--45. doi:10.1007/BF02384500.

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