  We study Hitchin representations and maximal symplectic representations of
surface groups, which can be both thought of as generalisations of Fuchsian
representations. We show that the corresponding energy functionals are proper
on Teichmuller space. We also prove that the mapping class group acts properly
on the corresponding moduli spaces. These two results follows from the fact
these representations are well displacing which is a consequence they are
associated to cross ratios. We state some applications.
