Let $ℒ$(x,u,∇u) be a Lagrangian periodic of period 1 in x1,...,xn,u. We shall study the non self intersecting functions u: Rn$\to$R minimizing $ℒ$; non self intersecting means that, if u(x0 + k) + j = u(x0) for some x0∈Rn and (k , j) ∈Zn × Z, then u(x) = u(x + k) + j$\forall$x. Moser has shown that each of these functions is at finite distance from a plane u = ρ$·$x and thus has an average slope ρ; moreover, Senn has proven that it is possible to define the average action of u, which is usually called $\beta \left(\rho \right)$ since...