Bending, entropy and proper affine actions of surface groups

We study the variation of complex length with respect to bending deformations of quasifuchsian groups. As one application, we exhibit an explicit open neighborhood of the Fuchsian locus in quasifuchsian space so that the only critical points of the entropy function in this neighborhood lie on the Fuchsian locus. As a second application, we exhibit an explicit open neighborhood of the Fuchsian locus so that the adjoint of every representation which is not Fuchsian is the linear part of a proper affine action on the Lie algebra of SL(2,C).