Metric spaces with unique tangents
arXiv:1012.2210
Abstract
We are interested in studying doubling metric spaces with the property that at some of the points the metric tangent is unique. In such a setting, Finsler-Carnot-Caratheodory geometries and Carnot groups appear as models for the tangents. The results are based on an analogue for metric spaces of Preiss's phenomenon: tangents of tangents are tangents.