Calculus of Variations and Geometric Measure Theory
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C. De Lellis - F. Pellandini

Genus bounds for minimal surfaces arising from min-max constructions.

created by delellis on 06 May 2011


Published Paper

Inserted: 6 may 2011

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

For the update version and eventual errata see the webpage http:/www.math.uzh.chdelellis


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.

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