4 papers
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…
Hölder spiral arcs
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and…
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…