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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

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Volume 2019, Issue 753

Issues

Embedded minimal surfaces of finite topology

William H. Meeks III / Joaquín PérezORCID iD: https://orcid.org/0000-0003-1877-8884
Published Online: 2017-03-16 | DOI: https://doi.org/10.1515/crelle-2017-0008

Abstract

In this paper we prove that a complete, embedded minimal surface M in 3 with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface M¯ with boundary punctured in a finite number of interior points and that M can be represented in terms of meromorphic data on its conformal completion M¯. In particular, we demonstrate that M is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior of M.

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About the article

Received: 2016-05-20

Revised: 2017-01-10

Published Online: 2017-03-16

Published in Print: 2019-08-01


Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1309236

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2014-52368-P

This material is based upon work of William H. Meeks III 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. The research of Joaquín Pérez was partially supported by MINECO/FEDER grant no. MTM2014-52368-P.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 753, Pages 159–191, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2017-0008.

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