Moduli of families of curves for conformal and quasiconformal mappings
The goal of the author is to present a reasonably selfcontained approach to the Ahlfors-Beurling extremal length method and its various applications to Teichmüller spaces and to the study of univalent functions. It is assumed that the reader is familiar with a graduate level course on complex analysis. In particular, conformal mappings are used extensively. In the beginning of the book the author gives a long review of the literature which he has used as source. Some of the important sources listed by the author are the monographs by \textit{J. Jenkins} [Trans. Am. Math. Soc. 88, 207-213 (1958; Zbl 0082.06201)], \textit{G. V. Kuz'mina} [''Moduli of families of curves and quadratic differentials'', Proc. Steklov Inst. Math. 139, 1-231 (1982; Zbl 0491.30013)], \textit{M. Ohtsuka} [Dirichlet problem, extremal length, and prime ends (1970; Zbl 0197.08404)] and \textit{K. Strebel} [Quadratic differentials (1984; Zbl 0547.30001)].
scientific article; zbMATH DE number 1776388