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Extremal conformal mappings and poles of quadratic differentials

P. M. Tamrazov


Abstract: Conformal metric properties of multiply-connected planar domains are studied that are related to conformal mappings into the number sphere; problems are solved involving the extremalization of the distance between the images of boundary components or level lines, the diameters of boundary components, modules, etc. These problems are distinguished by the fact that the quadratic differentials occurring in them have five distinct poles which are free of any essential restrictions.

UDC: 517.54

MSC: 30F45, 30C70, 30C20, 30C45, 30D30

Received: 06.06.1967

 English version: Mathematics of the USSR-Izvestiya, 1968, 2:5, 987–996

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