Abstract:
Results and applications of the method of modules in geometric function theory are presented. The method was originated by J. A. Jenkins,and further development proceeded in works of the Leningrad–St. Petersburg mathematical school. A retrospective description of the origin of the method is given, and the determining role of Jenkins in the development of the method of the extremal metric is pointed out.
Key words and phrases:extremal metric, quadratic differential, trajectory, module of curve family, reduced module, extremal decomposition.