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 $X$.

We study algebraic dependences of three meromorphic mappings which share few moving hyperplanes without counting multiplicity.

In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.