The embedded Calabi-Yau conjecture for finite genus Meeks III, William H. Pérez Muñoz, Joaquín Ros Mulero, Antonio Proper minimal surface Embedded Calabi-Yau problem Minimal lamination Limit end Injectivity radius function Locally simply connected This material is based upon work for the NSF under Award No. DMS - 1309236. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the NSF. Research partially supported by MINECO/FEDER grants no. MTM2014-52368-P and MTM2017-89677-P. Suppose M is a complete, embedded minimal surface in R3 with an infinite number of ends, finite genus and compact boundary. We prove that the simple limit ends of M have properly embedded representatives with compact boundary, genus zero and with constrained geometry. We use this result to show that if M has at least two simple limit ends, then M has exactly two simple limit ends. Furthermore, we demonstrate that M is properly embedded in R3 if and only ifM has at most two limit ends if and only ifM has a countable number of limit ends. 2021-10-15T10:26:56Z 2021-10-15T10:26:56Z 2018-06-08 info:eu-repo/semantics/article Published version: William H. Meeks III. Joaquín Pérez. Antonio Ros. "The embedded Calabi–Yau conjecture for finite genus." Duke Math. J. 170 (13) 2891 - 2956, 15 September 2021. [https://doi.org/10.1215/00127094-2020-0087] http://hdl.handle.net/10481/70882 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Duke University