The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings

For a normalized quasiregular pluriharmonic mapping $f$ of the unit ball $B^n$ of $\mathbb {C}^n$ into $\mathbb {C}^n$, we estimate the supremum of numbers $R$ such that some subdomain $\Omega$ of the ball is mapped by $f$ diffeomorphically onto some ball of radius $R$. Our estimates significantly improve earlier estimates, even in the case of harmonic functions in the disc.