A commentary on Teichmüller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale"

الأصل · EN

We provide a commentary on Teichmüller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale" (Extremal quasiconformal mappings of closed oriented Riemann surfaces), Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl. 1940, No.22, 1-197 (1940). The paper is quoted in several works, although it was read by very few people. Some of the results it contains were rediscovered later on and published without any reference to Teichmüller.In this commentary, we highlight the main results and the main ideas contained in that paper and we describe some of the important developments they gave rise to.The final version of this paper, together with the English translation of Teichmüller's paper, will apper in Volume V of the Handbook of Teichmüller theory (European Mathematical Society Publishing House, 2015).