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Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals. (Russian) Zbl 0633.30023

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

MSC:

30C75 Extremal problems for conformal and quasiconformal mappings, other methods
30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
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