  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 $f:D\rightarrow D^{\,\prime}$ are
extend to $\partial D$ whenever $\partial D$ is locally connected, $\partial
D^{\,\prime}$ is strongly accessible, and a function $Q$ has finite mean
oscillation at $\partial D.$
