  David maps are generalizations of classical planar quasiconformal maps for
which the dilatation is allowed to tend to infinity in a controlled fashion. In
this note we examine how these maps distort Hausdorff dimension. We show \vs
{enumerate} [$\bullet$] Given $\alpha$ and $\beta$ in $[0,2]$, there exists a
David map $\phi:\CC \to \CC$ and a compact set $\Lambda$ such that $\Hdim
\Lambda =\alpha$ and $\Hdim \phi(\Lambda)=\beta$. \vs [$\bullet$] There exists
a David map $\phi:\CC \to \CC$ such that the Jordan curve $\Gamma=\phi (\Sen)$
satisfies $\Hdim \Gamma=2$.\vs {enumerate} One should contrast the first
statement with the fact that quasiconformal maps preserve sets of Hausdorff
dimension 0 and 2. The second statement provides an example of a Jordan curve
with Hausdorff dimension 2 which is (quasi)conformally removable.
