Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity

Abstract

We introduce a weighted version of intermediate Ricci curvature and establish several equivalent characterizations of its lower bound. As an application, we generalize the results of Aishwarya--Rotem--Shenfeld [arXiv:2509.23399v1] by deriving intrinsic-dimensional evolution variational inequalities and the corresponding Wasserstein contraction estimates for the heat flow. We also compare our characterization with that of Ketterer--Mondino [arXiv:1610.03339v3] via lower-dimensional optimal transport.

60 pages