Journal of Differential Geometry

Min-max minimal hypersurfaces in non-compact manifolds

Rafael Montezuma

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 14 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1468517502

Digital Object Identifier
doi:10.4310/jdg/1468517502

Mathematical Reviews number (MathSciNet)
MR3523529

Zentralblatt MATH identifier
1377.53081

Citation

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


Export citation