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.

Voir la notice de l'article 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. 
@article{TM_2006_253_a11,
     author = {S. Yu. Orevkov},
     title = {Algebraic {Curve} in the {Unit} {Ball} in $\mathbb C^2$ {That} {Passes} through the {Origin} and {All} of {Whose} {Boundary} {Components} {Are} {Arbitrarily} {Short}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {135--157},
     publisher = {mathdoc},
     volume = {253},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a11/}
}
TY  - JOUR
AU  - S. Yu. Orevkov
TI  - Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 135
EP  - 157
VL  - 253
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2006_253_a11/
LA  - ru
ID  - TM_2006_253_a11
ER  - 
%0 Journal Article
%A S. Yu. Orevkov
%T Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 135-157
%V 253
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2006_253_a11/
%G ru
%F TM_2006_253_a11
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/

[1] Beloshapka V.K., “Ob odnom metricheskom svoistve analiticheskikh mnozhestv”, Izv. AN SSSR. Ser. mat., 40 (1976), 1409–1414 | Zbl

[2] Chirka E.M., “Nekotorye nereshennye zadachi mnogomernogo kompleksnogo analiza”, Kompleksnyi analiz v sovremennoi matematike, K 80-letiyu so dnya rozhdeniya B.V. Shabata, Fazis, M., 2001, 265–272 | MR

[3] Eroshkin O.G., “Ob odnom topologicheskom svoistve kraya analiticheskogo podmnozhestva strogo psevdovypukloi oblasti v $\mathbb C^2$”, Mat. zametki, 49:5 (1991), 149–151 | MR | Zbl

[4] Jöricke B., “A Cantor set in the unit sphere in $\mathbb C^2$ with large polynomial hull”, Michigan Math. J., 53 (2005), 189–207 | DOI | MR | Zbl