Construction of Hamilton sequences for certain Teichmüller mappings

Abstract:

Suppose $\sup \{ |\iint _{\left | z \right | < 1} {\kappa (z)\varphi (z)dxdy|:\varphi (z)}$ analytic for $\left | z \right | < 1,\iint _{\left | z \right | < 1} {|\varphi (z)|dxdy = 1\} = {\text {ess}}\sup }\{ |\kappa (z)|:\left | z \right | < 1\}$. The question of constructive determination of extremal sequences $\{ \varphi _n \}$ is considered for some classes of functions $\kappa (z)$ that arise in connection with plane quasiconformal mappings. For example, such a sequence $\{ \varphi _n \}$ is constructed explicitly for the $\kappa (z)$ that arises in connection with the affine stretch of Strebel’s chimney domain.