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Genus bounds for minimal surfaces arising from min-max constructions


De Lellis, C; Pellandini, F (2010). Genus bounds for minimal surfaces arising from min-max constructions. Journal für die Reine und Angewandte Mathematik, 2010(644):47-99.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:5 May 2010
Deposited On:23 Dec 2010 14:05
Last Modified:05 Apr 2016 14:27
Publisher:De Gruyter
ISSN:0075-4102
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1515/CRELLE.2010.052
Related URLs:http://www.math.uzh.ch/fileadmin/math/preprints/15_08.pdf
http://arxiv.org/abs/0905.4035

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