Smooth approximation, Alexandrov-Fenchel type inequalities and curvature flows for h-convex bodies in hyperbolic space

We associate each h-convex body in hyperbolic space $\mathbb{H}^{n+1}(n\geq 2)$ with a Radon measure valued $(0,2)$-tensor on the sphere $\mathbb{S}^n$ through its horospherical function. Using spherical convolution, we prove that any h-convex body can be approximated by a sequence of smooth strictl