Harmonic close-to-convex functions and minimal surfaces

In this paper, we study the family of sense-preserving complex-valued harmonic functions that are normalized close-to-convex functions on the open unit disk with. We derive a sufficient condition for to belong to the class. We take the analytic part of to be or and for a suitable choice of co-analytic part of, the second complex dilatation turns out to be a square of an analytic function. Hence, is lifted to a minimal surface expressed by an isothermal parameter. Explicit representation for classes of minimal surfaces are given. Graphs generated by using Mathematica are used for illustration. © 2013 Taylor & Francis.