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
Abstract

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.

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