A constructive method for starlike harmonic mappings
The authors expand an idea of the reviewer according to which certain conformal mappings f render a functional \(\nu\) (f) minimum within the class of all (suitably normalized) holomorphic functions. The authors extend this principle to functions f which satisfy a differential equation of Beltrami-type \(\bar f_{\bar z}(z)=a(z)f_ z(z)\). The advantage of this principle is its easy transition to numerical computations. The authors describe this method and present some examples \((a(z)=\rho z\) \((0<\rho <1)\), \(\nu (z)=Im z)\) for which they know the exact results. In the case of the chosen \(\nu\) the numerical procedure is reduced to linear programming. The numerical figures shown are at least partially quite accurate.
extremal principles for harmonic functions
scientific article; zbMATH DE number 4107160