Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity

Chao-Ming Lin; Kai-Hsiang Wang

Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity

Differential Geometry 2026-08-04 v1

Authors: Chao-Ming Lin , Kai-Hsiang Wang

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.

Keywords

weighted intermediate Ricci curvature entropy convexity evolution variational inequalities Wasserstein contraction heat flow

Cite

@article{arxiv.2608.03405,
  title  = {Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity},
  author = {Chao-Ming Lin and Kai-Hsiang Wang},
  journal= {arXiv preprint arXiv:2608.03405},
  year   = {2026}
}

Comments

60 pages