Hölder continuity of tangent cones in RCD(K,N) spaces and applications to non-branching

Abstract: It is known by a result of Colding-Naber that for any two points in a Ricci limit space, there exists a minimizing geodesic where the geometry of small balls centred along the interior of the geodesic change in at most a H\”older continuous manner. This was shown using an extrinsic argument and had several key applications for the structure theory of Ricci limits. In this talk, I will discuss how to generalize this result to the setting of metric measure spaces satisfying the synthetic lower Ricci curvature bound condition RCD(K,N). As an application, I will show that all RCD(K,N) spaces are non-branching, a fact which was previously unknown for Ricci limits.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

University of Toronto Geometry & Topology seminar