Abstract: For 3-dimensional 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

conditions for the constant mean curvature surface that bounds a compact manifold to guarantee

the positivity of its Hawking mass. We also establish estimates of the Bartnik mass of such surface,

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.