  In the setting of subFinsler Carnot groups, we consider curves that satisfy
the normal equation coming from the Pontryagin Maximum Principle. We show that,
unless it is constant, each such a curve leaves every compact set,
quantitatively. Namely, the distance between the points at time 0 and time $t$
grows at least of the order of $t^{1/s}$, where $s$ denotes the step of the
Carnot group. In particular, in subFinsler Carnot groups there are no periodic
normal geodesics.
