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

Li, Yangyang

doi:10.2140/gt.2022.26.2713

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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 $(M^{n + 1}, g)$ with $3 \leq n + 1 \leq 7$ 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

References

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

Volume 26, issue 6 (2022)