Abstract:
In this project, we construct harmonic shear ƒ n,m of elliptic integral F(z,1) = [equation] with dilation [equation] is an arbitrary natural number and m is a complex number such that | ≤ 1. In particu-lar case, we found that the image of D under ƒn;m is a parallelogram when | = 1. We then use the Weierstrass representation to construct a family of minimal graphs and prove that minimal graphs in this family are JS surfaces, minimal graphs over polygonal domains that become infinite in magnitude at the domain boundary.
