Minimal hypersurfaces with bounded index

作者：Chodosh Otis; Ketover Daniel; Maximo Davi^*

来源：Inventiones Mathematicae, 2017, 209(3): 617-664.

DOI：10.1007/s00222-017-0717-5

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.

• 出版日期2017-9