A different expression of the Weil-Petersson potential on the quasi-Fuchsian deformation space

We extend a definition of the Weil-Petersson potential on the universal Teichmuller space to the quasi-Fuchsian deformation space. We prove that up to a constant, this function coincides with the Weil-Petersson potential on the quasi-Fuchsian deformation space. As a result, we prove a lower bound for the Weil-Petersson potential on the quasi-Fuchsian deformation space.