5 papers
Bi-Lipschitz embeddings of quasiconformal trees
Guy C. David, Sylvester Eriksson-Bique, Vyron Vellis
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. In this paper we show…
On uniformly disconnected Julia sets
Alastair N. Fletcher, Vyron Vellis
It is well-known that the Julia set of a hyperbolic rational map is quasisymmetrically equivalent to the standard Cantor set. Using the uniformization theorem of David and Semmes,…
Hölder parameterization of iterated function systems and a self-affine phenomenon
Matthew Badger, Vyron Vellis
We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attra…
Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces
Vasileios Chousionis, Sean Li, Vyron Vellis +1
The Heisenberg group 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 embedd…
Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem
Matthew Badger, Lisa Naples, Vyron Vellis
We investigate the geometry of sets in Euclidean and infinite-dimensional Hilbert spaces. We establish sufficient conditions that ensure a set of points is contained in the image o…