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On
the existence of minimal hypersurfaces with arbitrarily large
area and Morse index
Yangyang Li |
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Geometry & Topology 26 (2022) 2713–2729
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DOI: 10.2140/gt.2022.26.2713
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Abstract |
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We show that a bumpy closed Riemannian manifold with 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. |
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Keywords
minimal surfaces, area, Morse index, min–max theory
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Mathematical Subject Classification
Primary: 53A10, 53C42
Secondary: 49Q05
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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
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Authors |
| Yangyang Li | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| https://yangyanglisite.com | |
