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.
|Original language||English (US)|
|Number of pages||45|
|Journal||Journal of Differential Geometry|
|State||Published - Jul 2016|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology