Calculus of Variations and Geometric Measure Theory

C. De Lellis - F. Pellandini

Genus bounds for minimal surfaces arising from min-max constructions

created by delellis on 06 May 2011
modified on 27 Jun 2019


Published Paper

Inserted: 6 may 2011
Last Updated: 27 jun 2019

Journal: J. Reine Angew. Math.
Volume: 644
Pages: 47-99
Year: 2010

ArXiv: 0905.4035 PDF

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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 Rubistein 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.