Comparison Theorems and the Intermediate Ricci Curvature Assumption
Differential Geometry
2025-10-14 v1
Abstract
We explore the notion of m-intermediate Ricci curvature assumption introduced by Brendle-Hirsch-Johne further. If a manifold has non-negative m-intermediate Ricci curvature and stable weighted slicing of order m-1, then the last slice has almost non-negative Ricci curvature in the spectral sense. We prove comparison theorems on the diameter and in-radius bound for stable weighted (respectively free boundary) slicing in such manifolds (respectively with mean convex boundary).
Cite
@article{arxiv.2510.11205,
title = {Comparison Theorems and the Intermediate Ricci Curvature Assumption},
author = {Yujie Wu},
journal= {arXiv preprint arXiv:2510.11205},
year = {2025}
}
Comments
15 pages. Comments welcome!