Geodesic
Polynomially convex hulls of families of arcs
Zbigniew S/lodkowski 1
1 Department of Mathematics (M//C 249) University of Illinois at Chicago 851 South Morgan Street Chicago, IL 60607-7045, U.S.A.
Studia Mathematica, Tome 165 (2004) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The paper is devoted to the study of polynomially convex hulls of compact subsets of ${\mathbb C}^2$, 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.
DOI : 10.4064/sm165-1-1
Keywords: paper devoted study polynomially convex hulls compact subsets mathbb fibered boundary unit disc fibers simple arcs plane their endpoints form boundaries closed intersecting analytic discs principal question concerned under what additional condition hull bordered topological hypersurface particular foliated unique holomorphic motion main results asserts happens family arcs satisfies continuous cone condition

Zbigniew S/lodkowski  1

1 Department of Mathematics (M//C 249) University of Illinois at Chicago 851 South Morgan Street Chicago, IL 60607-7045, U.S.A. 
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Zbigniew S/lodkowski. Polynomially convex hulls of families of arcs. Studia Mathematica, Tome 165 (2004) no. 1, pp. 1-17. doi: 10.4064/sm165-1-1

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