Sharp LpLp-entropy inequalities on manifolds

In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean LpLp-entropy inequalities for p>1p>1. In this work, we present some contributions in the Riemannian context. Namely, let (M,g)(M,g) be a compact Riemannian manifold of dimension n≥3n≥3. For 12p>2.