Extremal problems in classes of quasiconformal embeddings of Riemann surfaces (Q1876427)

The authors prove existence of the extremals of Belinskij functionals, weight dilatation, integral weight dilatation, and the energy integral; obtain conditions for their uniqueness in homotopic classes of quasiconformal embeddings of finite Riemann surfaces; and describe characteristic properties of extremal embeddings. This is an English translation of the authors' article published in the book [S. K. Vodop'yanov (ed.), Proceedings on Analysis and Geometry. International conference in honor of the 70th birthday of Professor Yu. G. Reshetnyak. Novosibirsk: Izdatel'stvo Instituta Matematiki (2000; Zbl 0971.00061)].