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Suppose sup{|I fJif<1 ic(z)cp(z) dx dyl: ep(z) analytic for Ilz < 1, ff,i 1<1 Ip (z)I dxdy = 1} = esssup{/IK(z)I: IzI < 1}. The question of constructive determination of extremal sequences { pv } is considered for some classes of functions /c(z) that arise in connection with plane quasiconformal mappings. For example, such a sequence {v eo} is constructed explicitly for the /c(z) that arises in connection with the affine stretch of Strebel's chimney domain.

Construction of Hamilton sequences for certain Teichmüller mappings