2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156848We prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kaehler metric on a compact Hermitian symmetric spaces of ABCD--type.Some corrections suggested by the referee. To appear on Annales de l'Institut FourierDifferential GeometryAlgebraic Geometrytext