Geodesic
On the existence of minimal hypersurfaces with arbitrarily large area and Morse index
Li, Yangyang1
1 Department of Mathematics, Princeton University, Princeton, NJ, United States
Geometry & topology, Tome 26 (2022) no. 6, pp. 2713-2729.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that a bumpy closed Riemannian manifold (Mn+1,g) with 3 ≤ n + 1 ≤ 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

Li, Yangyang 1

1 Department of Mathematics, Princeton University, Princeton, NJ, United States 
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Li, Yangyang. On the existence of minimal hypersurfaces with arbitrarily large area and Morse index. Geometry & topology, Tome 26 (2022) no. 6, pp. 2713-2729. http://geodesic.mathdoc.fr/item/GT_2022_26_6_a5/

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