A note on a unicity theorem for the Gauss maps of complete minimal   surfaces in Euclidean four-space
  The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness theorem for the Gauss maps of complete minimal surfaces in Euclidean four-space. 
Pham Hoang Ha and Yu Kawakami
math.DG math.CV