  This paper deals with locally constrained inverse curvature flows in a broad
class of Riemannian warped spaces. For a certain class of such flows we prove
long time existence and smooth convergence to a radial coordinate slice. In the
case of two-dimensional surfaces and a suitable speed, these flows enjoy two
monotone quantities. In such cases new Minkowski type inequalities are the
consequence. In higher dimensions we use the inverse mean curvature flow to
obtain new Minkowski inequalities when the ambient radial Ricci curvature is
constantly negative.
