Spacelike minimal surfaces which are graphs in [formula omitted

Abstract

In this work we study a system of two second order nonlinear partial differential equations corresponding to the equations of minimal spacelike graphs in the four-dimensional Minkownski space R14. We obtain a set of entire solutions of these equations, adapting the method of Karl Kommerell used for the analogous problem in R4. In our technique we replace ‘‘graphs of holomorphic functions” by ‘‘graphs of generalized harmonic curves” and then we obtain a class of minimal spacelike surfaces in R14 which are also entire graphs with non-zero Gauss curvature. We then provide two versions of the Bernstein Theorem corresponding for the two types of graphs which can occur in R14. Several explicit examples are given.