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math.CV2026
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…
math.CV2026
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…
math.CV2026
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…