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 Zap. Nauchn. Sem. LOMI, 1987, Volume 160, Pages 121–137 (Mi znsl5429)

Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals

G. V. Kuz'mina

Abstract: 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).

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Bibliographic databases:

Document Type: Article
UDC: 517.54

Citation: G. V. Kuz'mina, “Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals”, Analytical theory of numbers and theory of functions. Part 8, Zap. Nauchn. Sem. LOMI, 160, "Nauka", Leningrad. Otdel., Leningrad, 1987, 121–137

Citation in format AMSBIB
\Bibitem{Kuz87} \by G.~V.~Kuz'mina \paper Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals \inbook Analytical theory of numbers and theory of functions. Part~8 \serial Zap. Nauchn. Sem. LOMI \yr 1987 \vol 160 \pages 121--137 \publ "Nauka", Leningrad. Otdel. \publaddr Leningrad \mathnet{http://mi.mathnet.ru/znsl5429} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=869526} \zmath{https://zbmath.org/?q=an:0900.30029|0633.30023}