  We give a proof by foliation that the cones over $\mathbb{S}^k \times
\mathbb{S}^l$ minimize parametric elliptic functionals for each $k,\,l \geq 1$.
We also analyze the behavior at infinity of the leaves in the foliations. This
analysis motivates conjectures related to the existence and growth rates of
nonlinear entire solutions to equations of minimal surface type that arise in
the study of such functionals.
