We define lines of minima in the thick part of Outer space for the free group
Fn with n>2 generators. We show that these lines of minima are contracting for
the Lipschitz metric. Every fully irreducible outer automorphism of Fn defines
such a line a minima. Now let G be a subgroup of the outer automorphism group
of Fn which is not virtually abelian. We obtain as an immediate application
that if G contains at least one fully irreducible element then for every p<1
the second bounded cohomology group with coefficients in lp(G) is infinite
dimensional.