  We prove several Liouville theorems for F-harmonic maps from some complete
Riemannian manifolds by assuming some conditions on the Hessian of the distance
function, the degrees of F(t) and the asymptotic behavior of the map at
infinity. In particular, the results can be applied to F-harmonic maps from
some pinched manifolds, and can deduce a Bernstein type result for an entire
minimal graph.
