On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index
Differential Geometry
2023-05-08 v3 Geometric Topology
Abstract
We show that a bumpy closed Riemannian manifold admits a sequence of connected closed embedded two-sided minimal hypersurfaces whose areas and Morse indices both tend to infinity. This improves a previous result by O. Chodosh and C. Mantoulidis on connected minimal hypersurfaces with arbitrarily large area.
Cite
@article{arxiv.2001.07689,
title = {On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index},
author = {Yangyang Li},
journal= {arXiv preprint arXiv:2001.07689},
year = {2023}
}
Comments
Final version, to appear in Geom. Topol