  This paper establishes bounds on the homogenized surface tension for a
heterogeneous Allen-Cahn energy functional in a periodic medium. The approach
is based on relating the homogenized energy to a purely geometric variational
problem involving the large scale behaviour of the signed distance function to
a hyperplane in periodic media. Motivated by this, a homogenization result for
the signed distance function to a hyperplane in both periodic and almost
periodic media is proven.
