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 
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/
@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},
     year = {1987},
     volume = {160},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a11/}
}
TY  - JOUR
AU  - G. V. Kuz'mina
TI  - Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1987
SP  - 121
EP  - 137
VL  - 160
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a11/
LA  - ru
ID  - ZNSL_1987_160_a11
ER  - 
%0 Journal Article
%A G. V. Kuz'mina
%T Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals
%J Zapiski Nauchnykh Seminarov POMI
%D 1987
%P 121-137
%V 160
%U http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a11/
%G ru
%F ZNSL_1987_160_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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).