On Natário's Minkowski-type inequality in the hyperbolic space

We apply Brendle–Guan–Li's inverse curvature–type flow to prove a family of sharp inequalities for curvature integrals and their rigidity results for hypersurfaces in the hyperbolic space. In particular, we provide a new short proof of Natário's Minkowski-type inequality and its rigidity for convex surfaces in the hyperbolic 3-space.