Mathematische Annalen

, Volume 357, Issue 3, pp 1049–1070 | Cite as

Every bordered Riemann surface is a complete proper curve in a ball

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Abstract

We prove that every bordered Riemann surface admits a complete proper holomorphic immersion into a ball of \(\mathbb C ^2\), and a complete proper holomorphic embedding into a ball of \(\mathbb C ^3\).

Mathematics Subject Classification (2000)

32B15 32H02 14H50 53C42 
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Notes

Acknowledgments

A. Alarcón is supported by Vicerrectorado de Política Científica e Investigación de la Universidad de Granada, and is partially supported by MCYT-FEDER grants MTM2007-61775 and MTM2011-22547, Junta de Andalucía Grant P09-FQM-5088, and the grant PYR-2012-3 CEI BioTIC GENIL (CEB09-0010) of the MICINN CEI Program. F. Forstnerič is supported by the research program P1-0291 from ARRS, Republic of Slovenia.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Faculty of Mathematics and Physics, Institute of Mathematics, Physics and MechanicsUniversity of LjubljanaLjubljanaSlovenia

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