Minimal hyperspheres of arbitrarily large Morse index
Differential Geometry
2015-04-09 v1
Abstract
We show that the Morse index of a closed minimal hypersurface in a four-dimensional Riemannian manifold cannot be bound in terms of the volume and the topological invariants of the hypersurface itself by presenting a method for constructing Riemannian metrics on S^4 that admit embedded minimal hyperspheres of uniformly bounded volume and arbitrarily large Morse index. The phenomena we exhibit are in striking contrast with the three-dimensional compactness results by Choi-Schoen.
Keywords
Cite
@article{arxiv.1504.02066,
title = {Minimal hyperspheres of arbitrarily large Morse index},
author = {Alessandro Carlotto},
journal= {arXiv preprint arXiv:1504.02066},
year = {2015}
}