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Every bordered Riemann surface is a complete proper curve in a ball
Authors:Antonio Alarcón  Franc Forstnerič
Affiliation:1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain
2. Faculty of Mathematics and Physics, Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
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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