Projective Hulls and Characterizations of Meromorphic Functions
  We give conditions characterizing holomorphic and meromorphic functions in the unit disk of the complex plane in terms of certain weak forms of the maximum principle. Our work is directly inspired by recent results of John Wermer, and by the theory of the projective hull of a compact subset of complex projective space developed by Reese Harvey and Blaine Lawson. 
J.T. Anderson, J.A. Cima, N. Levenberg and T.J. Ransford
math.CV