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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843588

Digital Object Identifier
doi:10.2140/apde.2017.10.1987

Mathematical Reviews number (MathSciNet)
MR3694012

Zentralblatt MATH identifier
1384.32014

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

Keywords
complex curves holomorphic embeddings complete bounded submanifolds

Citation

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. https://projecteuclid.org/euclid.apde/1510843588


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