Vol. 10, No. 8, 2017

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Complete embedded complex curves in the ball of $\mathbb{C}^2$ can have any topology

Antonio Alarcón and Josip Globevnik

Vol. 10 (2017), No. 8, 1987–1999

In this paper we prove that the unit ball B of 2 admits complete properly embedded complex curves of any given topological type. Moreover, we provide examples containing any given closed discrete subset of B.

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complex curves, holomorphic embeddings, complete bounded submanifolds
Mathematical Subject Classification 2010
Primary: 32H02, 32B15, 32C22
Received: 27 January 2017
Accepted: 29 June 2017
Published: 18 August 2017
Antonio Alarcón
Departamento de Geometría y Topología e Instituto de Matemáticas (IEMath-GR)
Universidad de Granada
Josip Globevnik
Department of Mathematics and Institute of Mathematics, Physics and Mechanics
University of Ljubljana