First stability eigenvalue of singular minimal hypersurfaces in spheres
Differential Geometry
2016-12-06 v2
Abstract
In this short note we extend an estimate due to J. Simons on the first stability eigenvalue of minimal hypersurfaces in spheres to the singular setting. Specifically, we show that any singular minimal hypersurface in , which is not totally geodesic and satisfies the \alpha-structural hypothesis, has first stability eigenvalue at most -2n, with equality if and only if it is a product of two round spheres. The equality case was settled independently in the classical setting by Wu and Perdomo.
Cite
@article{arxiv.1610.04816,
title = {First stability eigenvalue of singular minimal hypersurfaces in spheres},
author = {Jonathan J. Zhu},
journal= {arXiv preprint arXiv:1610.04816},
year = {2016}
}
Comments
13 pages; added references and a construction of Morgan-Ritore. arXiv admin note: text overlap with arXiv:1607.07760