On the index of minimal hypersurfaces in ${\mathbb{S}}^{n+1}$ with ${\lambda }_1<n$

Hang Chen, Peng Wang

In this paper, we prove that a closed minimal hypersurface in $\SSS$ with ${\lambda }_1<n$ has Morse index at least $n+4$, providing a partial answer to a conjecture of Perdomo. As a coroll…