On the Hawking mass for CMC surfaces in positive curved 3-manifolds

In this paper, we present two rigidity results for stable constant mean curvature (CMC) surfaces immersed in $3$-manifolds with positive scalar curvature, assuming that the Hawking mass is zero. In the first result, we assume the surface to be approximately round, while in the second result, we consider surfaces invariant under an even symmetry.