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math.DS2026
Uniformization of Julia sets of geometrically finite rational maps
Yusheng Luo, Dimitrios Ntalampekos
A Schottky set is the complement of a collection of disjoint open disks in the Riemann sphere. We completely characterize geometrically finite rational maps whose Julia sets are qu…
math.CV2026
Conformal rigidity: progress and challenges
Dimitrios Ntalampekos, Malik Younsi
A domain in the Riemann sphere is called a \textit{circle domain} if every connected component of its boundary is either a round circle or a single point. A circle domain is \texti…
math.CV2026
Koebe uniformization, John domains, and transboundary modulus
Christina Karafyllia, Dimitrios Ntalampekos
We prove Koebe's conjecture for John domains by showing that every planar John domain is conformally equivalent to a circle domain. Our proof is based on a geometric property of Jo…