Hardy's inequality for W1,p0-functions on Riemannian manifolds

We prove that for every Riemannian manifold chi with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class W-0(1,p)(chi). We also study manifolds satisfying Hardy's inequality and, in particular, we establish an estimate for the rate of growth of the weighted volume of the noncompact part of such a manifold.