  Following earlier work of Loftin-McIntosh, we study minimal Lagrangian
immersions of the universal cover of a closed surface (of genus at least 2)
into CH2, with prescribed data of a conformal structure plus a holomorphic
cubic differential. We show existence and non-uniqueness of such minimal
Lagrangian immersions. We also establish the surface area with respect to the
induced metric as a Weil-Petersson potential function for the space of
holomorphic cubic differentials on the Riemann surface.
