744 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
Some properties of H\"older surfaces in the Heisenberg group
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder
surface in the subRiemannian Heisenberg group. Namely, it is expected that
there is no embedding from an open subset of R^2 into the Heisenberg group that
is Hoelder continuous of order strictly greater than 1/2. The Heisenberg group
here is equipped with its Carnot-Caratheodory distance. We show that, in the
case that such a surface exists, it cannot be of essential bounded variation
and it intersects some vertical line in at least a topological Cantor set.Comment: 18 pages, 1 figur
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