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July 2016 Min-max minimal hypersurfaces in non-compact manifolds
Rafael Montezuma
J. Differential Geom. 103(3): 475-519 (July 2016). DOI: 10.4310/jdg/1468517502

Abstract

In this work we prove the existence of embedded closed minimal hypersurfaces in non-compact manifolds containing a bounded open subset with smooth and strictly mean-concave boundary and a natural behavior on the geometry at infinity. For doing this, we develop a modified min-max theory for the area functional following Almgren and Pitts’ setting, to produce minimal hypersurfaces with intersecting properties. In particular, we prove that any strictly mean-concave region of a compact Riemannian manifold without boundary intersects a closed minimal hypersurface.

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Rafael Montezuma. "Min-max minimal hypersurfaces in non-compact manifolds." J. Differential Geom. 103 (3) 475 - 519, July 2016. https://doi.org/10.4310/jdg/1468517502

Information

Published: July 2016
First available in Project Euclid: 14 July 2016

zbMATH: 1377.53081
MathSciNet: MR3523529
Digital Object Identifier: 10.4310/jdg/1468517502

Rights: Copyright © 2016 Lehigh University

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Vol.103 • No. 3 • July 2016
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