The paper is devoted to the study of polynomially convex hulls of compact subsets of ℂ², fibered over the boundary of the unit disc, such that all fibers are simple arcs in the plane and their endpoints form boundaries of two closed, not intersecting analytic discs. The principal question concerned is under what additional condition such a hull is a bordered topological hypersurface and, in particular, is foliated by a unique holomorphic motion. One of the main results asserts that this happens when the family of arcs satisfies the Continuous Cone Condition.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-1,
author = {Zbigniew S\l odkowski},
title = {Polynomially convex hulls of families of arcs},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {1-17},
zbl = {1056.32012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-1}
}
Zbigniew Słodkowski. Polynomially convex hulls of families of arcs. Studia Mathematica, Tome 162 (2004) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-1-1/