In this talk, we introduce the notion of -harmonic map with respect to the -energy functional . In the first part, We prove the Liouville type theorems for these -harmonic maps. By using an extrinsic average variational method in the calculus of variations we obtain that any stable -harmonic maps must be constant from compact -SSU manifold into Riemannian manifold or from any compact manifold into compact -SSU manifold. In the second part, we study the heat flow of -harmonic maps into spheres. For every sphere-valued initial map in the energy space, we prove the global existence of a weak solution to the Cauchy Dirichlet problem with time-independent boundary values.