Conformal uniformization of domains bounded by quasitripods
Abstract
We prove Koebe’s conjecture and a version of Schramm’s cofat uniformization theorem for domains Ω⊂Cˆ satisfying conditions involving quasitripods, that is, quasisymmetric images of the standard tripod. If the nonpoint complementary components of Ω contain uniform quasitripods with large diameters and satisfy a packing condition, then there exists a conformal map f:Ω→D onto a circle domain D. Moreover, f preserves the classes of point-components and nonpoint-components. The packing condition is satisfied if Ω is cospread, that is, if the complementary components contain uniform quasitripods in all scales.
Fields of Study & Subjects
Analytic and geometric function theory
Holomorphic and Operator Theory
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 4
- Publication date
- 13 February 2026