Minimal hypersurfaces with bounded index

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 $$(M^{n},g)$$ ( M n , g ) , $$3\le n\le 7$$ 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. Inventiones mathematicae Springer Journals

Minimal hypersurfaces with bounded index

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Mathematics; Mathematics, general
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