Quasiconformal extremals of the energy integral (Q1898510)

The commented paper exemplifies the validity of the heuristic Teichmüller principle according to which some extremal problems of the theory of functions become analytical quadratic differentials. The principal results of the paper state that the harmonic maps and also extremals of energy integral in homotopic classes of the \(K\)-quasi-conformal homeomorphisms of flat domains and Riemann surfaces of hyperbolic type at values \(K\) exceeding the quasiconformity coefficient of the homotopy class are connected in natural way with pairs of holomorphic quadratic differentials as it takes place for the case of the Teichmüller map.