English

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).

Keywords

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!

R2 v1 2026-07-01T06:33:34.516Z