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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138493Let $M$ be a closed hypersurface in a simply connected rank-1 symmetric space $\olm$. In this paper, we give an upper bound for the first eigenvalue of the Laplacian of $M$ in terms of the Ricci curvature of $\olm$ and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of $M$.9 pagesDifferential GeometryMetric Geometry53C40, 53C42, 53C20A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spacestext