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

Format:

Book

Author/Creator:

Vasilʹev, Alexander, 1962-

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1788.

Lecture notes in mathematics, 0075-8434 ; 1788

Language:

English

Subjects (All):

Functions of complex variables.

Moduli theory.

Conformal mapping.

Curves.

Riemann surfaces.

Physical Description:

ix, 211 pages : illustrations ; 23 cm.

Place of Publication:

Berlin ; New York : Springer, [2002]

Summary:

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmller spaces.

Notes:

Includes bibliographical references (pages [197]-206) and index.

ISBN:

3540438467

OCLC:

50072382