Extreme points method and univalent harmonic mappings

We consider the class of all sense-preserving complex-valued harmonic mappings f = h + g defined on the unit disk D with the normalization h(0) = h′ (0) − 1 = 0 and g(0) = g′ (0) = 0 with the second complex dilatation ω: D → D, g′ (z) = ω(z)h′ (z). In this paper, the authors determine sufficient conditions on h and ω that would imply the univalence of harmonic mappings f = h + g on D.