×

On the question of extremal properties of quadratic differentials with end domains in the structure of trajectories. (Russian) Zbl 0692.30019

Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 168, 98-113 (1988).
[For the entire collection see Zbl 0657.00006.]
Quadratic differentials play an essential role in several types of extremal problems. Here the author studies the role of quadratic differentials with poles of order \(\geq 3\) in the context of extremal partitioning problems. She states that this paper represents a preliminary investigation. The author works with the notion of the reduced modulus of domains that are related to strip- and end-domains. (This reduced modulus was inroduced in [G. V. Kuz’mina, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 154, 110-129 (1986; Zbl 0608.30027)] and in [E. G. Emel’yanov, ibid. 154, 76-89 (1986; Zbl 0608.30026)].) The author obtains results extremal partitionings of these domains.
Reviewer: Renate McLaughlin

MSC:

30C75 Extremal problems for conformal and quasiconformal mappings, other methods
Full Text: EuDML