Algebraic curve in the unit ball in C^2 passing through the center, all whose boundary components are arbitrarily short

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105062We 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.Complex VariablesGeometric TopologyAlgebraic curve in the unit ball in C^2 passing through the center, all whose boundary components are arbitrarily shorttext