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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 2017: 1.686

CiteScore 2017: 0.96

SCImago Journal Rank (SJR) 2017: 2.585
Source Normalized Impact per Paper (SNIP) 2017: 1.203

Mathematical Citation Quotient (MCQ) 2016: 1.28

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Volume 2010, Issue 644


Genus bounds for minimal surfaces arising from min-max constructions

Camillo De Lellis / Filippo Pellandini
Published Online: 2010-05-31 | DOI: https://doi.org/10.1515/crelle.2010.052


In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubinstein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.

About the article

Received: 2008-10-30

Published Online: 2010-05-31

Published in Print: 2010-07-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2010, Issue 644, Pages 47–99, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2010.052.

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