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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 \(\mathbb C ^3\).

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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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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071 , Granada, Spain

    Antonio Alarcón

  2. Faculty of Mathematics and Physics, Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 , Ljubljana, Slovenia

    Franc Forstnerič

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  1. Antonio Alarcón
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  2. Franc Forstnerič
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Correspondence to Franc Forstnerič.

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Alarcón, A., Forstnerič, F. Every bordered Riemann surface is a complete proper curve in a ball. Math. Ann. 357, 1049–1070 (2013). https://doi.org/10.1007/s00208-013-0931-4

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  • DOI: https://doi.org/10.1007/s00208-013-0931-4

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