Abstract
Abstract In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.
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