We consider extensions of quasiconformal maps and the uniformization theorem to the
setting of metric spaces X homeomorphic to R 2. Given a measure μ on such a space, we …

We construct bi-Lipschitz embeddings into Euclidean space for bounded-diameter subsets
of manifolds and orbifolds of bounded curvature. The distortion and dimension of such …

A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded
above by a fixed multiple of the distance between its endpoints. We study the geometry of …

We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it
is metrically quasiconformal and if and only if it is geometrically quasiconformal. As the main …

$ SRA $-free spaces is a wide class of metric spaces including finite dimensional
Alexandrov spaces of non-negative curvature, complete Berwald spaces of nonnegative flag …

Quantitative Embeddability and Connectivity in Metric Spaces Page 1 Quantitative
Embeddability and Connectivity in Metric Spaces by Sylvester David Eriksson-Bique A …

The Heisenberg group $\mathbb {H} $ equipped with a sub-Riemannian metric is one of the
most well known examples of a doubling metric space which does not admit a bi-Lipschitz …

În prezenta Teza de Doctorat este investigata geometria unor structuri subriemanniene de
rang variabil, cunoscute sub numele de varietati de tip Grushin, precum si problema …

Abstract Given α> 0, the α-Grushin plane is R2 equipped with the sub-Riemannian metric
generated by the vector fields X=∂ 1 and Y=| x1| α∂ 2. It is a standard example in sub …