Minimal hypersurfaces with bounded index
Differential Geometry
2019-07-01 v4 Geometric Topology
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 of dimension at most seven, 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 follows our local picture.
Cite
@article{arxiv.1509.06724,
title = {Minimal hypersurfaces with bounded index},
author = {Otis Chodosh and Daniel Ketover and Davi Maximo},
journal= {arXiv preprint arXiv:1509.06724},
year = {2019}
}
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