Natural generalizations of minimal surfaces and prescribed mean curvature surfaces in higher dimension, are given by n-harmonic maps and their variations such as H-systems. These maps are governed by n-Laplace systems with antisymmetric potentials. Regularity properties of those systems are difficult to obtain for two reasons : first because the leading order operator is nonlinear and second because the system is critical from the point of view of the standard regularity theory. I will discuss some progress obtained in a joint work with Armin Schikorra.
