Algebraic curve in the unit ball in ℂ2 that passes through the origin and all of whose boundary components are arbitrarily short

Proceedings of the Steklov Institute of Mathematics - Tập 253 Số 1 - Trang 123-143 - 2006
Orevkov, S. Yu.1,2
1Université Paul Sabatier (Toulouse III), Toulouse cedex 4, France
2Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Tóm tắt

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.

Tài liệu tham khảo

citation_journal_title=Izv. Akad. Nauk SSSR, Ser. Mat.; citation_title=On a Metric Property of Analytic Sets; citation_author=V. K. Beloshapka; citation_volume=40; citation_publication_date=1976; citation_pages=1409-1414; citation_id=CR1 citation_title=Some Unsolved Problems in Multidimensional Complex Analysis; citation_inbook_title=Complex Analysis in Modern Mathematics: To the 80th Birthday of B.V. Shabat; citation_publication_date=2001; citation_pages=265-272; citation_id=CR2; citation_author=E. M. Chirka; citation_publisher=Fazis citation_journal_title=Zametki; citation_title=On a Topological Property of the Boundary of an Analytic Subset of a Strictly Pseudoconvex Domain in ℂ2 ; citation_author=O. G. Eroshkin; citation_volume=49; citation_issue=5; citation_publication_date=1991; citation_pages=149-151; citation_id=CR3 citation_journal_title=Mich. Math. J.; citation_title=A Cantor Set in the Unit Sphere in ℂ2 with Large Polynomial Hull; citation_author=B. Jöricke; citation_volume=53; citation_publication_date=2005; citation_pages=189-207; citation_doi=10.1307/mmj/1114021092; citation_id=CR4