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Smooth families of fibrations and analytic selections of polynomial hulls

Published online by Cambridge University Press:  17 April 2009

Miran Černe
Miran Černe
Affiliation:
University of LjubljanaIMFM Jadranska 1961 111 LjubljanaSlovenia
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Abstract

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Constructed are strictly increasing smooth families Σt ⊆ ∂D × C2, t ∈ [0, 1], of fibrations over the unit circle with strongly pseudoconvex fibers all diffeomorphic to the ball such that there is no analytic selection of the polynomial hull of Σ0 and which end at the product fibration . In particular these examples show that the continuity method for describing the polynomial hull of a fibration over ∂D fails even if the complex geometry of the fibers is relatively simple.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 97 - 105
Copyright
Copyright © Australian Mathematical Society 1995

References

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