  In this paper we study the existence and the dynamics of a very special class
of motions, which satisfy a strong global minimization property. More
precisely, we call a free time minimizer a curve which satisfies the least
action principle between any pair of its points without the constraint of time
for the variations. An example of a free time minimizer defined on an unbounded
interval is a parabolic homothetic motion by a minimal central confguration.
The existence of a large amount of free time minimizers can be deduced from the
weak KAM theorem. In particular, for any choice of x0, there should be at least
one free time minimizer x(t) defined for all positive time and satisfying
x(0)=x0. We prove that such motions are completely parabolic. Using Marchal's
theorem we deduce as a corollary that there are no entire free time minimizers,
i.e. defined on R. This means that the Ma\~n\'e set of the Newtonian N-body
problem is empty.
