A lower bound for the first eigenvalue of a minimal hypersurface in the sphere

Asun Jiménez, Carlos Tapia Chinchay, Detang Zhou

Let $\Sigma$ be a closed embedded minimal hypersurface in the unit sphere ${\mathbb{S}}^{m+1}$ and let $\Lambda =\underset{\Sigma }{\max }|A|$ be the norm of its second fundamental form. In this work we pro…