Lower $N$-weighted Ricci curvature bound with $\varepsilon$-range and displacement convexity of entropies

Abstract

In this article, we provide a characterization of a lower N -weighted Ricci curvature bound for N ∈] − ∞, 1] ∪ [n, +∞] with ε-range in terms of a convexity of entropies over Wasserstein space.