A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces

Let $M$ be a closed hypersurface in a simply connected rank-1 symmetric space $\text{olm}$. In this paper, we give an upper bound for the first eigenvalue of the Laplacian of $M$ in terms of the Ricci curvature of $\text{olm}$ and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of $M$.