2024/01/16 by Behnam Esmayli, Esmayli, Behnam, Kai Rajala +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2401.08485
openalex publication_date 2024/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains Ω⊂ \mathbb C satisfying conditions involving quasitripods, i.e., quasisymmetric images of the standard tripod. If the non-point complementary components of Ω contain uniform quasitripods with large diameters and satisfy a packing condition, then there exists a conformal map f\colonΩ→ D onto a circle domain D. Moreover, f preserves the classes of point-components and non-point components. The packing condition is satisfied if Ω is cospread, i.e., if the complementary components contain uniform quasitripods in all scales.