8 papers · 1 filter
Quasisymmetric rectifiability of uniformly disconnected sets
Jacob Honeycutt, Vyron Vellis
We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological…
Universal quasiconformal trees
Efstathios Konstantinos Chrontsios Garitsis, Fotis Ioannidis, Vyron Vellis
A quasiconformal tree is a doubling (compact) metric tree in which the diameter of each arc is comparable to the distance of its endpoints. We show that for each integer ,…
Hölder curves with exotic tangent spaces
Eve Shaw, Vyron Vellis
An important implication of Rademacher's Differentiation Theorem is that every Lipschitz curve infinitesimally looks like a line at almost all of its points in the sense that a…
Bi-Lipschitz arcs in metric spaces with controlled geometry
Jacob Honeycutt, Vyron Vellis, Scott Zimmerman
We generalize a bi-Lipschitz extension result of David and Semmes from Euclidean spaces to complete metric measure spaces with controlled geometry (Ahlfors regularity and supportin…
Parametrizability of infinitely generated attractors
Eve Shaw, Vyron Vellis
An infinite iterated function system (IIFS) is a countable collection of contraction maps on a compact metric space. In this paper we study the conditions under which the attractor…
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…