Minimal hypersurfaces with bounded index

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 ( M n , g ) , 3 ≤ n ≤ 7 , can degenerate. Loosely speaking,...

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Veröffentlicht in:Inventiones mathematicae 2017-09, Vol.209 (3), p.617-664
Hauptverfasser: Chodosh, Otis, Ketover, Daniel, Maximo, Davi
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ( M n , 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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-017-0717-5