Geodesic
Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 135-157 
S. Yu. Orevkov. Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 135-157. http://geodesic.mathdoc.fr/item/TM_2006_253_a11/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A negative answer is given to the following question of A. G. Vitushkin: Does there exist a nontrivial lower bound for the length of the maximal component of intersection of the unit sphere and an algebraic curve passing through the origin.

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