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April 2002 Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration
Miran Černe
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Ark. Mat. 40(1): 27-45 (April 2002). DOI: 10.1007/BF02384500

Abstract

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).

Funding Statement

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

Citation

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Miran Černe. "Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration." Ark. Mat. 40 (1) 27 - 45, April 2002. https://doi.org/10.1007/BF02384500

Information

Received: 25 April 2000; Revised: 22 June 2001; Published: April 2002
First available in Project Euclid: 31 January 2017

zbMATH: 1039.32014
MathSciNet: MR1948884
Digital Object Identifier: 10.1007/BF02384500

Rights: 2002 © Institut Mittag-Leffler

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