  Characterizations of entire subsolutions for the 1-harmonic equation of a
constant 1$-tension field are given with applications in geometry via
transformation group theory. In particular, we prove that every level
hypersurface of such a subsolution is calibrated and hence is area-minimizing
over $\mathbb{R}$; and every 7-dimensional $SO(2)\times SO(6)$-invariant
absolutely area-minimizing integral current in $\mathbb{R}^8$ is real analytic.
The assumption on the $SO(2) \times SO(6)$-invariance cannot be removed, due to
the first counter-example in $\mathbb{R}^8$, proved by Bombieri, De Girogi and
Giusti.
