Min-max minimal hypersurfaces in non-compact manifolds

Rafael Montezuma

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageAmerican English
Pages (from-to)475-519
Number of pages45
JournalJournal of Differential Geometry
Issue number3
StatePublished - Jul 2016

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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