2-regular points in 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.

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