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

@article{Alarcn2013EveryBR,
  title={Every bordered Riemann surface is a complete proper curve in a ball},
  author={A. Alarc{\'o}n and F. Forstneri{\vc}},
  journal={Mathematische Annalen},
  year={2013},
  volume={357},
  pages={1049-1070}
}
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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