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In this paper, we prove Perelman type $\mathcal{W}$-entropy formulae andglobal differential Harnack estimates for positive solutions to porous mediumequation on the closed Riemannian manifolds with Ricci curvature bounded below.As applications, we derive Harnack inequalities and Laplacian estimates.

$\mathcal{W}$-Entropy formulae and differential Harnack estimates for porous medium equations on Riemannian manifolds