Moduli of families of curves for conformal and quasiconformal mappings / Alexander Vasilʹev

The book is concerned with the extremal length method and some of its applications to extremal problems for conformal and quasiconformal mappings, and the extension of moduli onto Teichmüller spaces. In the words of the author, "this work is neither a complete exposition of the classical theory nor a complete survey of the latest results. But we hope one can find here a step to new ways of investigation to make progress in modern and classical problems.'' The book is divided into five chapters with a bibliography of 181 publications. Chapter 1 is an introduction. The headings of Chapters 2 to 5 are: Moduli of families of curves and extremal partitions, Moduli in extremal problems for conformal mappings, Moduli in extremal problems for quasiconformal mappings and Moduli on Teichmüller spaces. ... (MathSciNet)