The Ahlfors-Weill reflection on convex domains and Nehari quasidisks

The estimate $$\text{RR}\{a_{2}f\}>-\frac{1}{2}$$ derived for convex mappings in \cite{FMR}, is interpreted here in terms of the Ahlfors-Weill reflection to show that for such domains $\text{Om}$, the mediatrix of the segment $[w,{\text{mR}}_w]$ joining a point $w\in \text{Om}$ and its reflection ${\text{mR}}_w$ lies always outside $\text{Om}$. In particular, the midpoint of the segment is also outside $\text{Om}$. We determine the extremal cases when such a midpoint can lie of the boundary $\mathrm{\partial }\text{Om}$. The normalization $\text{fd}=\frac{f}{1+a_{2}f}$ to a Möbius equivalent mapping with vanishing second coefficient leads to important distinctions between bounded an unbounded domains. We finally derive a geometric characterization of Nehari quasidisks in terms of the distance to the boundary of the Ahlfors-Weill reflection.