English

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

Differential Geometry 2023-05-08 v3 Geometric Topology

Abstract

We show that a bumpy closed Riemannian manifold (Mn+1,g)(M^{n+1}, g) (3n+17)(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 on connected minimal hypersurfaces with arbitrarily large area.

Keywords

Cite

@article{arxiv.2001.07689,
  title  = {On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index},
  author = {Yangyang Li},
  journal= {arXiv preprint arXiv:2001.07689},
  year   = {2023}
}

Comments

Final version, to appear in Geom. Topol