Sharp L-p-entropy inequalities on manifolds

摘要

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