Extreme points method and univalent harmonic mappings

We consider the class of all sense-preserving complex-valued harmonic mappings $f=h+\bar{g}$ defined on the unit disk $\text{ID}$ with the normalization $h(0)=h^{\mathrm{\prime }}(0)-1=0$ and $g(0)=g^{\mathrm{\prime }}(0)=0$ with the second complex dilatation $\omega :\text{ID}\to \text{ID}$, $g^{\mathrm{\prime }}(z)=\omega (z)h^{\mathrm{\prime }}(z)$. In this paper, the authors determine sufficient conditions on $h$ and $\omega$ that would imply the univalence of harmonic mappings $f=h+\bar{g}$ on $\text{ID}$.