Journal of Differential Geometry

Min-max minimal hypersurfaces in non-compact manifolds

Rafael Montezuma

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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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J. Differential Geom., Volume 103, Number 3 (2016), 475-519.

First available in Project Euclid: 14 July 2016

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Montezuma, Rafael. Min-max minimal hypersurfaces in non-compact manifolds. J. Differential Geom. 103 (2016), no. 3, 475--519. doi:10.4310/jdg/1468517502.

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