Minimal hypersurfaces with bounded index

Otis Chodosh, Daniel Ketover, Davi Maximo

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (Mn, g) , 3 ≤ n≤ 7 , can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems follow from our local picture.

Original languageEnglish (US)
Pages (from-to)617-664
Number of pages48
JournalInventiones Mathematicae
Volume209
Issue number3
DOIs
StatePublished - Sep 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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