Flat Projective Structures on Surfaces and Cubic Holomorphic   Differentials
  The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge theory. We shall also give an application of these results as the uniqueness of a minimal surface in a symmetric space. 
F. Labourie