
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.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities
