3 citations · 3 across the 5 of their papers we have counts for
7 papers
Uniformization problems in the plane: A survey
Dimitrios Ntalampekos
In this survey we present the history and recent progress on several fundamental (quasi)conformal uniformization problems in the complex plane. Uniformization refers to the process…
Characterization of tangent quasicircles and quasiannuli
Dimitrios Ntalampekos
We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain…
Quasiconformal characterization of Schottky sets
Dimitrios Ntalampekos
The complement of the union of a collection of disjoint open disks in the -sphere is called a Schottky set. We prove that a subset of the -sphere is quasiconformally equi…
Characterization of quasispheres via smooth approximation
Dimitrios Ntalampekos
We prove that every two-dimensional quasisphere is the limit of a sequence of smooth spheres that are uniform quasispheres. In the case of metric spheres of finite area we provide…
Uniformization of gasket Julia sets
Yusheng Luo, Dimitrios Ntalampekos
The object of the paper is to characterize gasket Julia sets of rational maps that can be uniformized by round gaskets. We restrict to rational maps without critical points on the…
Piecewise quasiconformal dynamical systems of the unit circle
Yusheng Luo, Dimitrios Ntalampekos
We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or…
David extension of circle homeomorphisms, welding, mating, and removability
Mikhail Lyubich, Sergei Merenkov, Sabyasachi Mukherjee +1
We provide a David extension result for circle homeomorphisms conjugating two dynamical systems such that parabolic periodic points go to parabolic periodic points, but hyperbolic…