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On the existence of minimal hypersurfaces with arbitrarily large area and Morse index

### Yangyang Li

Geometry & Topology 26 (2022) 2713–2729
DOI: 10.2140/gt.2022.26.2713
##### Abstract

We show that a bumpy closed Riemannian manifold $\left({M}^{n+1},g\right)$ with $3\le n+1\le 7$ 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 (Int. Math. Res. Not. (2021) 10841–10847) on connected minimal hypersurfaces with arbitrarily large area.

##### Keywords
minimal surfaces, area, Morse index, min–max theory
##### Mathematical Subject Classification
Primary: 53A10, 53C42
Secondary: 49Q05
##### Publication
Received: 30 August 2020
Revised: 11 June 2021
Accepted: 12 July 2021
Published: 13 December 2022
Proposed: Tobias H Colding
Seconded: John Lott, Dmitri Burago
##### Authors
 Yangyang Li Department of Mathematics Princeton University Princeton, NJ United States https://yangyanglisite.com