Hardy type inequalities on complete Riemannian manifolds

Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces

“…Application of this is that a complete non-compact M with a non-negative Bakry-Émery tensor satisfying Hardy-type inequalities with the best constant is not far to the Euclidean space of the same dimension. This agrees with [34] where the same results were established for a complete non-compact Riemannian manifold with a non-negative Ricci tensor. Recently, there was another attempt made by the authors in [35], where they extended some inequalities derived in [5] to the setting of smooth metric measure spaces.…”

Hardy type inequalities on the sphere

“…Hardy inequalities are a subfamily of the Caffarelli-Kohn-Nirenberg inequalities. In a Riemannian manifold, the knowledge of the validity of these inequalities and their best constants allows us to obtain qualitative properties on the manifold [ 7 – 10 ].…”

The Caffarelli-Kohn-Nirenberg Inequalities on Metric Measure Spaces

“…In [1,2,9,10,16,30,31], the authors consider the study of Riemannian manifolds with non-negative Ricci curvature supporting some of the particular classes of CKN. In particular, in [1,2,9,30,31], the authors obtain some metric and topological rigidity results.…”