Some properties of the functions of the form $v\left(x\right)={\sum }_{i=0}^m{\left|x\right|}^i{h}_i\left(x\right)$ in ℝⁿ, n ≥ 2, where each $h_i$ is a harmonic function defined outside a compact set, are obtained using the harmonic measures.

This paper establishes a hypersurface defect relation, that is, ${\sum }_{j=1}^q\delta (D_j,f)\le (n+1)/d$, for a family of meromorphic maps from a generalized p-parabolic manifold M to the projective space ℙⁿ, under some weak non-degeneracy assumptions.

We consider a nondegenerate holomorphic map $f:V\mapsto X$ where $(X,\omega )$ is a compact Hermitian manifold of dimension larger than or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$. In this article we give criteria which permit to construct Ahlfors’ currents in $X$.