On boundary behavior of one class of mappings on Riemannian manifolds

Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained. In particular, there is proved that, open discrete ring $Q$-mappings $f:D\to D^{\mathrm{\prime }}$ are extend to $\mathrm{\partial }D$ whenever $\mathrm{\partial }D$ is locally connected, $\partial D^{,\prime}$isstronglyaccessible,andafunction$Q$ has finite mean oscillation at $\mathrm{\partial }D\mathrm{.}$