We will study the space of proper holomorphic mappings between balls in different dimensions. To every proper mapping we can associate a finite rank hermitian form. As the resulting space is be convex, it is natural to define a convex family of proper mappings. While there are many proper mappings in codimension one when there is no further assumption, we will prove there is no convex family in codimension one. Stronger results can be proven when one restricts the maps to the monomial category. This is joint work with John D'Angelo.