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.

Final version, to appear in Geom. Topol

Cited by in corpus (1)

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