On the First Eigenvalue of Embedded Minimal Hypersurfaces in the Unit Sphere

Abstract

Let $\hat{I}\pounds$ be a closed embedded minimal hypersurface in ${\mathbb{S}}^{n+1}$. We establish an improved lower bound for the first non-zero eigenvalue of the induced Laplace-Beltrami operator on $\hat{I}\pounds$. It is slightly better than the bound of Duncan-Sire-Spruck.