Analysis & PDE

  • Anal. PDE
  • Volume 10, Number 8 (2017), 1987-1999.

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

Antonio Alarcón and Josip Globevnik

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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.

Article information

Anal. PDE, Volume 10, Number 8 (2017), 1987-1999.

Received: 27 January 2017
Accepted: 29 June 2017
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 32B15: Analytic subsets of affine space 32C22: Embedding of analytic spaces

complex curves holomorphic embeddings complete bounded submanifolds


Alarcón, Antonio; Globevnik, Josip. Complete embedded complex curves in the ball of $\mathbb{C}^2$ can have any topology. Anal. PDE 10 (2017), no. 8, 1987--1999. doi:10.2140/apde.2017.10.1987.

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