Algebraic curve in the unit ball in C^2 passing through the center, all whose boundary components are arbitrarily short
Complex Variables
2007-05-23 v1 Geometric Topology
Abstract
We prove that curves indicated in the title exist. This results answers to a question posed by A.G.Vitushkin about 30 years ago. We also discuss the minimal number of boundary components of a curve in the unit ball passing through the center, under the condition that all these components are shorter than a given number. More precisely, we discuss the order of growth of the number of the components as their maximal length tends to zero.
Cite
@article{arxiv.math/0511592,
title = {Algebraic curve in the unit ball in C^2 passing through the center, all whose boundary components are arbitrarily short},
author = {S. Yu. Orevkov},
journal= {arXiv preprint arXiv:math/0511592},
year = {2007}
}