Abstract

If S is the graph of a minimal surface, then when given parametrically by the Weierstrass representation, the first two coordinate functions give a univalent harmonic mapping. In this paper, the starting point is a univalent harmonic mapping f of the unit disk U. A height function is defined on an appropriate Riemann surface over the range of f which satisfies the minimal surface equation away from the branch points. This height function is then used to obtain function theoretic information about f.

Authors