# 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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