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Given a complete, connected Riemannian manifold $ \mathbb{M}^n $ with Riccicurvature bounded from below, we discuss the stability of the solutions of aporous medium-type equation with respect to the 2-Wasserstein distance. Weproduce (sharp) stability estimates under negative curvature bounds, which tosome extent generalize well-known results by Sturm and Otto-Westdickenberg. Thestrategy of the proof mainly relies on a quantitative $L^1-L^\infty$ smoothingproperty of the equation considered, combined with the Hamiltonian approachdeveloped by Ambrosio, Mondino and Savar\'e in a metric-measure setting.

Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below