A result of Geroch implies that Hawking mass satisfies an important monotonicity condition. Namely, if \mathcal{M}^3 has nonnegative scalar curvature, then the Hawking mass of \Sigma is non-decreasing as the surface \Sigma flows outward at a speed equal to the inverse of the mean curvature. In particular, if \Sigma_t is a family of connected surfaces evolving according to
