Isoperimetric type problems and Alexandrov–Fenchel type inequalities in the hyperbolic space

In this paper, we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space HnHn, by using quermassintegral preserving curvature flows. As a byproduct, we obtain hyperbolic Alexandrov–Fenchel inequalities.