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On symmetric configurations in some problems on extremal decomposition. II. (English. Russian original) Zbl 1182.30033

J. Math. Sci., New York 157, No. 4, 632-645 (2009); translation from Zap. Nauchn. Semin. POMI 357, 158-179 (2008).
Summary: Some problems on extremal decomposition in families of non-overlapping domains containing systems of biangles with free vertices on a circle are considered. Simultaneously, some progress in solving the classical problem on the maximum of a well-known conformal invariant is achieved. This exhibits the role of symmetric configurations in extremal problems under consideration.
[For part I, cf. Zap. Nauchn. Semin. POMI 350, 160–172 (2007)].

MSC:

30C75 Extremal problems for conformal and quasiconformal mappings, other methods
30C35 General theory of conformal mappings
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