731 research outputs found
A metric characterization of Carnot groups
We give a short axiomatic introduction to Carnot groups and their
subRiemannian and subFinsler geometry. We explain how such spaces can be
metrically described as exactly those proper geodesic spaces that admit
dilations and are isometrically homogeneous
Metric spaces with unique tangents
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
Closed BLD-elliptic manifolds have virtually Abelian fundamental groups
We show that a closed, connected, oriented, Riemannian -manifold,
admitting a branched cover of bounded length distortion from , has
a virtually Abelian fundamental group
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