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

Miran Černe Department of Mathematics, University of Ljubljana

TBD mathscidoc:1701.332972

Arkiv for Matematik, 40, (1), 27-45, 2000.4
Let$X$(-ϱ$B$^{$m$}×$C$^{$n$}be a compact set over the unit sphere ϱ$B$^{$m$}such that for each$z$∈ϱ$B$^{$m$}the fiber$X$_{$z$}={ω∈$C$^{$n$};($z, ω$)∈$X$} is the closure of a completely circled pseudoconvex domain in$C$^{$n$}. 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 ($z$_{0},$w$_{0})∈Int $$\hat X$$ there exists a smooth up to the boundary analytic disc$F$:Δ→$B$^{$m$}×$C$^{$n$}with the boundary in$X$such that$F$(0)=($z$_{0},$w$_{0}).
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@inproceedings{miran2000maximal,
  title={Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration},
  author={Miran Černe},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603369806781},
  booktitle={Arkiv for Matematik},
  volume={40},
  number={1},
  pages={27-45},
  year={2000},
}
Miran Černe. Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration. 2000. Vol. 40. In Arkiv for Matematik. pp.27-45. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603369806781.
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