  We investigate a version of Alberti's rank one theorem in Ahlfors regular
metric spaces, as well as a connection with quasiconformal mappings. More
precisely, we give a proof of the rank one theorem that partially follows along
the usual steps, but the most crucial step consists in showing for $f\in
BV(X;Y)$ that at $\Vert Df\Vert^s$-a.e. $x\in X$, the mapping $f$ ``behaves
non-quasiconformally''.
