A family of harmonic superspaces associated with four-dimensional Minkowski spacetime is described. Applications are given to free mass-less supermultiplets, invariant integrals and super Yang-Mills. The generalisation to curved spacetimes is given with emphasis on confor-mal supergravities.

A 2p-times continuously differentiable complex-valued function f = u+ iv in a simply connected domainΩ ⊆ C is p-harmonic if f satisfies the p-harmonic equation ∆p f = 0. In this paper, we investigate the properties of p-harmonic mappings in the unit disk |z| < 1. First, we discuss the convexity, the starlikeness and the region of variability of some classes of p-harmonic mappings. Then we prove...