  We show that log-concavity is the weakest power concavity preserved by the
Dirichlet heat flow in $N$-dimensional convex domains, where $N\ge 2$ (indeed,
we prove that starting with a negative power concave initial datum may result
in losing immediately any reminiscence of concavity). Jointly with what we
already know, i.e. that log-concavity is the strongest power concavity
preserved by the Dirichlet heat flow, we see that log-concavity is indeed the
only power concavity preserved by the Dirichlet heat flow.
