2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162428In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discover some new entropy formulae for these equations.22 pages, no figureDifferential GeometryAnalysis of PDEs53C44; 58J35text