The embedded Calabi-Yau conjecture for finite genus
Identificadores
URI: http://hdl.handle.net/10481/70882Metadatos
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Duke University
Materia
Proper minimal surface Embedded Calabi-Yau problem Minimal lamination Limit end Injectivity radius function Locally simply connected
Date
2018-06-08Referencia bibliográfica
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]
Patrocinador
NSF under Award No. DMS - 1309236; MINECO/FEDER grants no. MTM2014-52368-P and MTM2017-89677-PRésumé
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.