Recent progress on the regularity of n-harmonic maps

Abstract: The full regularity of harmonic maps from a given surface into an arbitrary Riemannian manifold has been proved by Hélein in 1991. This is not true anymore when the domain has dimension strictly greater than 2, Rivière constructed an example of harmonic map from a 3-dimensional domain which is everywhere discontinuous in 1995. There are many possible generalizations of these maps to the higher dimensional case in order to recover the regularity of some "optimal" maps. For most of these generalizations, the full regularity in the general case is still open. In this talk, we will discuss some recent progress obtained for n-harmonic maps. This is a joint work with Armin Schikorra.