English

2-regular points in Ricci limit spaces

Differential Geometry 2025-05-20 v2

Abstract

In this note, we will show that if a measured Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with lower Ricci curvature bound contains a 2-regular point which lies in the interior of a geodesic, then it is 2-rectifiable. And we will also give some properties about 2-regular points.

Keywords

Cite

@article{arxiv.2406.08306,
  title  = {2-regular points in Ricci limit spaces},
  author = {Lina Chen},
  journal= {arXiv preprint arXiv:2406.08306},
  year   = {2025}
}

Comments

Theorem 1.2 in the first version has been dropped for the gap found in Theorem 1.3. More precisely, in the proof of (1.3.3), the injective can not be derived by a a similar argument as in Proposition 3.1

R2 v1 2026-06-28T17:03:15.654Z