Title | Genus bounds for minimal surfaces arising from min-max constructions. |
Publication Type | Journal Article |
Year of Publication | 2010 |
Authors | De Lellis C., Pellandini F. |
Journal | Journal für die Reine und Angewandte Mathematik |
Volume | 2010 |
Pagination | 47–99 |
Date Published | May |
Publisher | Grelle |
Type of Article | geometric measure theory |
ISSN | 0075-4102 |
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. |
Notes | J. Reine Angew. Math. 644 (2010), 47–99. |
URL | https://www.degruyter.com/abstract/j/crll.2010.2010.issue-644/crelle.2010.052/crelle.2010.052.xml |
DOI | 10.1515/crelle.2010.052 |
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