Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces

We prove that if fᵖⁿ(C) is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree d>(n+1)max-p,1\, then its image is contained in a linear subspace of dimension at most [n-1/2]. Analog in the logarithmic case is also given. Our result strengthens a classical result of Green and provides a Nevanlinna theoretic proof for a recent result due to Etesse.