Equivalence of optimal $L^1$-inequalities on Riemannian Manifolds

Jurandir Ceccon, Leandro Cioletti

Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n\ge 2$. This paper concerns to the validity of the optimal Riemannian $L^1$-Entropy inequality \[ {\bf Ent}_{dv…