Uniform domains and capacity
Since the 1960's some particular classes of domains, such as John domains and quasiconformal images of disks, have been studied extensively. These classes have played an important role in geometric function theory, because several theorems, previously known for quasiconformal mappings of the unit disk can be extended to such more general domains. The authors study uniform domains in the Euclidean \(n\)-space and give a characterization in terms of geometric-potential theoretic conditions. Whitney cubes, moduli of curve families, and conformal capacities are among the key tools.
scientific article; zbMATH DE number 5186235