  We discuss various representations of planar $p$-harmonic systems of
equations and their solutions. For coordinate functions of $p$-harmonic maps we
analyze signs of their Hessians, the Gauss curvature of $p$-harmonic surfaces,
the length of level curves as well as we discuss curves of steepest descent.
The isoperimetric inequality for the level curves of coordinate functions of
planar $p$-harmonic maps is proven. Our main techniques involve relations
between quasiregular maps and planar PDEs. We generalize some results due to P.
Lindqvist, G. Alessandrini, G. Talenti and P. Laurence.
