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

Abstract

Let $Σ$ 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 $Σ$. It is slightly better than the bound of Duncan-Sire-Spruck.