2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66741In this paper we prove that the Kähler-Einstein metrics for a toroidal canonical degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-Einstein metric on the smooth part of the central fiber when the base locus of the degeneration family is empty. We also prove the incompleteness of the Weil-Peterson metric in this case.The assumption of simple in the toroidal degeneration is removed using base extensionDifferential Geometrytext