We apply the Riemannian Penrose inequality and the Riemannian positive mass theorem to derive inequalities on the boundary of a class of compact Riemannian
3
3
-manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e., a
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2
-sphere with positive constant mean curvature; and the rest of the boundary, if nonempty, consists of closed minimal surfaces. A key step in our proof is the construction of a collar extension that is inspired by the method of Mantoulidis-Schoen.