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15 September 2021 The embedded Calabi–Yau conjecture for finite genus
William H. Meeks III, Joaquín Pérez, Antonio Ros
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Duke Math. J. 170(13): 2891-2956 (15 September 2021). DOI: 10.1215/00127094-2020-0087

Abstract

Suppose that 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 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 if M has at most two limit ends if and only if M has a countable number of limit ends.

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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

Information

Received: 11 June 2019; Revised: 10 November 2020; Published: 15 September 2021
First available in Project Euclid: 27 August 2021

Digital Object Identifier: 10.1215/00127094-2020-0087

Subjects:
Primary: 53A10
Secondary: 49Q05, 53C42

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 13 • 15 September 2021
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