Kuz’mina, G. V. Existence of quadratic differentials with prescribed properties. (English. Russian original) Zbl 0908.30023 J. Math. Sci., New York 89, No. 1, 996-1007 (1998); translation from Zap. Nauchn. Semin. POMI 226, 120-137 (1996). In the first section of this paper, about the existence and extremal properties of quadratic differentials with trajectories that are similar to logarithmic spirals, the author corrects errors in one of her earlier papers [Extremal properties of quadratic differentials with trajectories which are asymptotically similar to logarithmic spirals, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 121-137 (1987; Zbl 0633.30023)]. The second section, about the existence of certain quadratic differentials with poles of high-order, continues and extends the author’s previous work. Beginning with quadratic differentials \(Q(z,\varepsilon)dz^2\) that satisfy a number of conditions, the author constructs quadratic differentials \(Q(z)dz^2\) with prescribe simple poles and poles of higher orders and such that some other conditions are satisfied. Reviewer: Renate McLaughlin (Flint) Cited in 1 ReviewCited in 1 Document MSC: 30C75 Extremal problems for conformal and quasiconformal mappings, other methods Keywords:logarithmic spirals; trajectories; quadratic differentials; poles of higher orders Citations:Zbl 0633.30023 PDFBibTeX XMLCite \textit{G. V. Kuz'mina}, J. Math. Sci., New York 89, No. 1, 996--1007 (1996; Zbl 0908.30023); translation from Zap. Nauchn. Semin. POMI 226, 120--137 (1996) Full Text: DOI References: [1] J. A. Jenkins, ”On the existence of certain general metrics. I, II,”Ann. Math.,66, 440–453 (1957);Tôhoku Math. J. (2),45, 247–257 (1993). · Zbl 0082.06301 [2] G. V. Kuz’mina, ”Modules of familes of curves and quadratic differentials,”Tr. Mat. Inst. Akad. Nauk SSSR,139, 1–240 (1980). [3] K. Strebel,Quadratic Differentials (Ergeb. Math. ihre Grenzgeb. 3 F., Bd 5), Springer-Verlag, Berlin (1984). [4] E. G. Emel’yanov, ”On the problem of extremal decomposition,”Zap. Nauchn. Semin. LOMI,154, 76–89 (1986). [5] G. V. Kuz’mina, ”On the extremal properties of quadratic differentials with strip domains in the structure of trajectories,”Zap. Nauchn. Semin. LOMI,154, 110–129 (1986). [6] E. G. Emel’yanov, ”On a connection between two problems of extremal decomposition,”Zap. Nauchn. Semin. LOMI,160, 91–98 (1988). [7] G. V. Kuz’mina, ”On the problem of extremal decomposition of the Riemann sphere,”Zap. Nauchn. Semin. LOMI,185, 72–95 (1990). [8] G. V. Kuz’mina, ”On extremal properties of quadratic differentials with trajectories asymptotically similar to logarithmic spirals,”Zap. Nauchn. Semin. LOMI,160, 121–137 (1987). [9] G. V. Kuz’mina, ”On the existence of quadratic differentials with poles of high orders,”Zap. Nauchn. Semin. POMI,212, 129–138 (1994). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.