Geodesic
Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 121-137

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One considers the module problem for a family $\mathcal{H}$ of homotopy classes $H_i$ of curves on the $z$-sphere $\bar{ \mathbb{C} }$, where some of the classes $H_i$ consist of curves which in the neighborhoods of the distinguished points on $\bar{ \mathbb{C} }$ behave asymptotically similar to logarithmic spirals. The connection of the indicated extremal metric problem with the problem on the extremal partitioning of $\bar{ \mathbb{C} }$ is established. This paper complements a previous theorem of the author (Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Vol. 154, pp. 110–129, 1986). 
@article{ZNSL_1987_160_a11,
     author = {G. V. Kuz'mina},
     title = {Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--137},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a11/}
}
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G. V. Kuz'mina. Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 121-137. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a11/