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Theorems on continuous extension on boundary for one class of open discretemappings between Riemannian manifolds are obtained. In particular, there isproved that, open discrete ring $Q$-mappings $f:D\rightarrow D^{\,\prime}$ areextend to $\partial D$ whenever $\partial D$ is locally connected, $\partialD^{\,\prime}$ is strongly accessible, and a function $Q$ has finite meanoscillation at $\partial D.$

On boundary behavior of one class of mappings on Riemannian manifolds