Extremal decompositions of Riemann surfaces and quasiconformal mappings of special form (Q5941886)

The author considers a finite type Riemann surface \(R\) decomposed into a set of cylindres, together with a system of positive numbers associated to these cylinders, and he describes the extremal functional which gives rise to the Teichmüller extremal map \(R\to R'\), as defined by Jenkins and Strebel, which is associated to such a decomposition. In the case where the surface is equal to the complex plane with a finite number of distinguished points (or punctures), he proves that the extremal functional is a pluriharmonic function of the coordinates of the distinguished points.