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.
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: | 29 Jul 2020 23:24 |
| 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