2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152281Using an analogue of Myers' theorem for minimal surfaces and three dimensional topology, we prove the diameter sphere theorem for Ricci curvature in dimension three and a corresponding eigenvalue pinching theorem. This settles these two open problems for closed 3 manifolds with positive Ricci curvature since they are both false in dimensions greater than three.LaTex Form. To appear in J. Geom. AnalysisDifferential Geometry53C20, 53C42text