Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces

In this paper, we proved a sharp Minkowski type inequality in Cartan-Hadamard 3-spaces by harmonic mean curvature flow and improves the known estimates for total mean curvature in hyperbolic 3-space. In particular, we sharpened Ghomi-Spruck’s result. As a corollary, we also get a comparison theorem between total mean curvature in Cartan-Hadamard 3-spaces with that of the geodesic sphere in hyperbolic 3-space with constant curvature.