Min-max minimal hypersurfaces in non-compact manifolds

Rafael Montezuma

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)475-519
Number of pages45
JournalJournal of Differential Geometry
Volume103
Issue number3
DOIs
StatePublished - Jul 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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