Lower N-weighted Ricci curvature bound with 𝜀-range and displacement convexity of entropies

Abstract

In this paper, we provide a characterization of a lower [Formula: see text]-weighted Ricci curvature bound for [Formula: see text] with [Formula: see text]-range introduced by Lu–Minguzzi–Ohta [Comparison theorems on weighted Finsler manifolds and space-times with [Formula: see text]-range, Anal. Geom. Metr. Spaces 10(1) (2022) 1–30] in terms of a convexity of entropies over Wasserstein space. We further derive various interpolation inequalities and functional inequalities.