2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71821We give a new estimate on the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature and provide a solution for a conjecture of H. C. Yang.14 pages, Title changedDifferential GeometryAnalysis of PDEsPrimary 58J50, 35P15; Secondary 53C21The first Dirichlet Eigenvalue of a Compact Manifold and the Yang Conjecturetext