Improved Hardy inequalities on Riemannian manifolds

Abstract

We study the following version of Hardy-type inequality on a domain Ω in a Riemannian manifold : We provide sufficient conditions on and V for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, with p<N, with , , etc.