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
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