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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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 5 May 2010 |
| Deposited On: | 23 Dec 2010 14:05 |
| Last Modified: | 12 Jul 2025 03:40 |
| Publisher: | De Gruyter |
| ISSN: | 0075-4102 |
| OA Status: | Green |
| 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 |
De Lellis, C