On ring $Q$-mappings with respect to non-conformal modulus

The paper is devoted to the development of the theory of open discrete ring $Q$-mappings with respect to $p$-modulus in ${\Bbb R}^n$, $n\geqslant2$. For such mappings, it is established a distance distortion estimate of the logarithmic type. It is also established a measure estimate for the ball image. Finally, it is investigated the asymptotic behavior for homeomorphic mappings.