Algebraic curve in the unit ball in C² passing through the center, all whose boundary components are arbitrarily short

2005/11/23 by S. Yu. Orevkov, Orevkov, S. Yu.
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Meromorphic and Entire Functions #math.CV #math.GT

paper · pdf · doi:10.48550/arxiv.math/0511592

arxiv created 2005/11/23 · openalex publication_date 2005/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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