2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218469This paper has been withdrawn by the author for further modification.This paper has been withdrawnDifferential GeometryAnalysis of PDEs58J35, 53C44 (Primary) 35B05,35K55 (Secondary)Simple proofs of some results of Perelman on Ricci flowtext