Thick sets and quasisymmetric maps

Porous Sets and Quasisymmetric Maps

A set A in R" is called porous if there is a > 0 such that every ball B(x,r) contains a point whose distance from A is at least ar. We show that porosity is preserved by quasisymmetric maps, in particular, by bilipschitz maps. Local versions are also given.

Semi-θ-Open Sets and New Classes of Maps

A ug 1 99 1 Quasisymmetric Conjugacies Between Unimodal Maps

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

semi-θ-open sets and new classes of maps

Random Intersections of Thick Cantor Sets

Let C1, C2 be Cantor sets embedded in the real line, and let τ1, τ2 be their respective thicknesses. If τ1τ2 > 1, then it is well known that the difference set C1 − C2 is a disjoint union of closed intervals. B. Williams showed that for some t ∈ int(C1−C2), it may be that C1∩ (C2 + t) is as small as a single point. However, the author previously showed that generically, the other extreme is tru...