Polynomially convex hulls of families of arcs

Zbigniew Słodkowski. "Polynomially convex hulls of families of arcs." Studia Mathematica 165.1 (2004): 1-17. <http://eudml.org/doc/284395>.

@article{ZbigniewSłodkowski2004,
abstract = {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.},
author = {Zbigniew Słodkowski},
journal = {Studia Mathematica},
keywords = {polynomially convex hull; family of arcs; analytic discs; topological hypersurface; foliation},
language = {eng},
number = {1},
pages = {1-17},
title = {Polynomially convex hulls of families of arcs},
url = {http://eudml.org/doc/284395},
volume = {165},
year = {2004},
}

TY - JOUR
AU - Zbigniew Słodkowski
TI - Polynomially convex hulls of families of arcs
JO - Studia Mathematica
PY - 2004
VL - 165
IS - 1
SP - 1
EP - 17
AB - 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.
LA - eng
KW - polynomially convex hull; family of arcs; analytic discs; topological hypersurface; foliation
UR - http://eudml.org/doc/284395
ER -