124 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
Conformal equivalence of visual metrics in pseudoconvex domains
We refine estimates introduced by Balogh and Bonk, to show that the boundary
extensions of isometries between smooth strongly pseudoconvex domains in \C^n
are conformal with respect to the sub-Riemannian metric induced by the Levi
form. As a corollary we obtain an alternative proof of a result of Fefferman on
smooth extensions of biholomorphic mappings between pseudoconvex domains. The
proofs are inspired by Mostow's proof of his rigidity theorem and are based on
the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on
the Bonk-Schramm hyperbolic fillings.Comment: 20 page
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