Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2
  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. 
Zheng Huang, John Loftin and Marcello Lucia
math.DG math.AP