Journal of Differential Geometry
- J. Differential Geom.
- Volume 103, Number 3 (2016), 475-519.
Min-max minimal hypersurfaces in non-compact manifolds
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.
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. https://projecteuclid.org/euclid.jdg/1468517502