On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index

Abstract

We show that a bumpy closed Riemannian manifold $(M^{n+1},g)$ $(3\le n+1\le 7)$ 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 on connected minimal hypersurfaces with arbitrarily large area.

arXiv commentFinal version, to appear in Geom. Topol

References in corpus (4)

• Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
• Existence of infinitely many minimal hypersurfaces in closed manifolds
• Min-max theory for free boundary minimal hypersurfaces I - regularity theory
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Cited by in corpus (1)

• Generic scarring for minimal hypersurfaces along stable hypersurfaces