Modulus techniques in geometric function theory
In geometric function theory, the (conformal) modulus of a ring (an annulus) is a key notion to analyze the local behavior of a mapping; for instance, quasiconformal mappings can be characterized in terms of the moduli of annuli. The article under review is an expository account on quasiconformal mappings and conformal homeomorphism with an emphasis on the role played by the modulus of an annulus or a semi-annulus. The author exhibits techniques to derive useful properties of the mappings by observing the modulus change of annuli under homeomorphism of a certain kind. To achieve that the readers get acquainted with modulus techniques, the proofs for some of the typical and important results are presented. Several recent results on conformal homeomorphism are also given in the article.
scientific article; zbMATH DE number 5976802
scientific article