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2016 Helicoidal minimal surfaces of prescribed genus
David Hoffman, Martin Traizet, Brian White
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Acta Math. 216(2): 217-323 (2016). DOI: 10.1007/s11511-016-0139-z

Abstract

For every genus g, we prove that S2×R contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the S2 tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in R3 that are helicoidal at infinity. We prove that helicoidal surfaces in R3 of every prescribed genus occur as such limits of examples in S2×R.

Funding Statement

The research of the second author was partially supported by ANR-11-ISO1-0002. The research of the third author was supported by NSF grants DMS–1105330 and DMS 1404282.

Citation

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David Hoffman. Martin Traizet. Brian White. "Helicoidal minimal surfaces of prescribed genus." Acta Math. 216 (2) 217 - 323, 2016. https://doi.org/10.1007/s11511-016-0139-z

Information

Received: 20 June 2013; Revised: 25 July 2015; Published: 2016
First available in Project Euclid: 30 January 2017

zbMATH: 1356.53010
MathSciNet: MR3573331
Digital Object Identifier: 10.1007/s11511-016-0139-z

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

Rights: 2016 © Institut Mittag-Leffler

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Vol.216 • No. 2 • 2016
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