  We study singularity formation for the heat flow of harmonic maps from
$\R^d$. For each $d \geq 4$, we construct a compact, $d$-dimensional,
rotationally symmetric target manifold that allows for the existence of a
corotational self-similar shrinking solution (shortly \emph{shrinker}) that
represents a stable blowup mechanism for the corresponding Cauchy problem.
