2-regular points in Ricci limit spaces

TL;DR

This paper proves that in Ricci limit spaces, the presence of a 2-regular point on a geodesic implies the space is 2-rectifiable, and explores properties of such points.

Contribution

It establishes the rectifiability of Ricci limit spaces containing 2-regular points on geodesics, advancing understanding of their geometric structure.

Findings

Presence of a 2-regular point on a geodesic implies 2-rectifiability.

Provides properties of 2-regular points in Ricci limit spaces.

Enhances understanding of the geometric structure of Ricci limit spaces.

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.