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.