2018-04-25 14:30-16:30 Room 1560, Science building No.1 We apply the Riemannian Penrose inequality and the Riemannian positive mass theorem to derive inequalities on the boundary of a class of compact Riemannian $3$-manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e. a $2$-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. These inequalities can be viewed as certain estimates of the Hawking mass. This talk is based on a joint work with Pengzi Miao at University of Miami.