Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration |
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Authors: | Miran Černe |
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Affiliation: | (1) Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia |
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Abstract: | LetX(-ϱB m ×C n be a compact set over the unit sphere ϱB m such that for eachz∈ϱB m the fiberX z ={ω∈C n ;(z, ω)∈X} is the closure of a completely circled pseudoconvex domain inC n . The polynomial hull ofX is described in terms of the Perron-Bremermann function for the homogeneous defining function ofX. Moreover, for each point (z 0,w 0)∈Int there exists a smooth up to the boundary analytic discF:Δ→B m ×C n with the boundary inX such thatF(0)=(z 0,w 0). This work was supported in part by a grant from the Ministry of Science of the Republic of Slovenia. |
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