Genus bounds for minimal surfaces arising from min-max constructions

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dc.creatorDe Lellis, Camillo
dc.creatorPellandini, Filippo
dc.date2009-05-25
dc.date.accessioned2026-07-07T13:17:56Z
dc.date.available2026-07-07T13:17:56Z
dc.descriptionIn 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.
dc.descriptionAccepted for publication on Journal for Pure and Applied Mathematics
dc.identifierhttps://arxiv.org/abs/0905.4035
dc.identifierhttp://arxiv.org/abs/0905.4035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231275
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.titleGenus bounds for minimal surfaces arising from min-max constructions
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