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 Tr. Mat. Inst. Steklova, 2006, Volume 253, Pages 135–157 (Mi tm90)

Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short

S. Yu. Orevkov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 123–143

Bibliographic databases:

UDC: 512.772+515.173.2

Citation: 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”, Complex analysis and applications, Collected papers, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 135–157; Proc. Steklov Inst. Math., 253 (2006), 123–143

Citation in format AMSBIB
\Bibitem{Ore06} \by S.~Yu.~Orevkov \paper Algebraic Curve in the Unit Ball in $\mathbb C^2$ That Passes through the Origin and All of Whose Boundary Components Are Arbitrarily Short \inbook Complex analysis and applications \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2006 \vol 253 \pages 135--157 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm90} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338694} \elib{http://elibrary.ru/item.asp?id=13530380} \transl \jour Proc. Steklov Inst. Math. \yr 2006 \vol 253 \pages 123--143 \crossref{https://doi.org/10.1134/S008154380602012X} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748319346} 

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This publication is cited in the following articles:
1. Joericke B., “Envelopes of holomorphy and holomorphic discs”, Inventiones Mathematicae, 178:1 (2009), 73–118
2. Chekanov Yu., Schlenk F., “Lagrangian product tori in symplectic manifolds”, Comment. Math. Helv., 91:3 (2016), 445–475
3. Joericke B., “Analytic Knots, Satellites and the 4-Ball Genus”, Math. Z., 286:1-2 (2017), 263–290
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