Constants and Characterization for Certain Classes of Univalent Harmonic Mappings

Abstract

In this paper, we obtain growth, covering, and area theorems for certain families of sense preserving univalent harmonic functions which are close-to-convex in the unit disk \({\mathbb{D}}\). We present integral representation for the class that we have considered for our study. Representation of minimal surface associated with this class is also given whenever the second complex dilatation is a square of an analytic function. Also, we determine a general sufficient condition for a sense preserving harmonic function to be univalent and close-to-convex in \({\mathbb{D}}\). Finally, we examine the disk of univalency and close-to-convexity of certain classes of harmonic functions.