Kuz’mina, G. V. Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals. (Russian) Zbl 0633.30023 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 121-137 (1987). The author continues and extends earlier investigations about extremal properties of quadratic differentials. Classes of curves are considered, which, in a neighborhood of distinguished points, are asymptotically similar to logarithmic spirals. The investigation begins with the assumption that there exists a quadratic differential \(Q(z)dz^ 2\) whose trajectories have the prescribed structure. Then the method of extremal metric is used to investigate module problems. Finally, the existence of \(Q(z)dz^ 2\) is established using Schiffer’s method of interior variations. Reviewer: Renate McLaughlin Cited in 2 ReviewsCited in 1 Document MSC: 30C75 Extremal problems for conformal and quasiconformal mappings, other methods 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods Keywords:quadratic differentials; extremal metric; module problems; interior variations PDFBibTeX XMLCite \textit{G. V. Kuz'mina}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 121--137 (1987; Zbl 0633.30023) Full Text: EuDML