Conformal uniformization and packings
The paper deals with uniformizations of domains in the extended complex plane using conformal mappings and domains with boundaries of prescribed shapes. The author gives a new proof of a uniformization result due to \textit{A. N. Harrington} [J. Anal. Math 41, 39-53 (1982; Zbl 0528.30006)], which relies on the topological notion of the degree of proper maps between manifolds. By taking limits of uniformized domains, where the shapes of boundaries of domains change in a controlled way, the author also proves the existence of packings of bodies with given shapes and with given tangency patterns. Finally, the uniqueness of packings and uniformized domains is addressed in the paper.
scientific article; zbMATH DE number 878303
scientific article