For a compact manifold, nonnegative scalar curvature always gives some obstructions to the quasi-local mass of the boundary. In this talk, we will give some intrinsic restrictions for the constant mean curvature hypersursurface that bounds a compact manifold with nonnegative scalar curvature. We will discuss the condition to guarantee the positivity of its Hawking mass. We also establish estimates of the Bartnik mass of such hypersurface, without assumptions on the integral of the squared mean curvature. Estimates on the hyperbolic Bartnik mass of surface are also considered when the ambient manifold has negative scalar curvature. This is a joint work with Pengzi Miao and Naqing Xie.

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