Generalized Sharp Hardy Type and Caffarelli-Kohn-Nirenberg Type Inequalities on Riemannian Manifolds

Shih-Shu Walter Wei ； Ye Li

《Tamkang Journal of Mathematics》 40卷4期 (2009/12) Pp. 401-413

並列摘要

We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds M. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold M (that is, not necessarily on a punctured manifold M\{x0} where x0 is a fixed point in M). Some topological and geometric applications are discussed.

並列關鍵字

Caffarelli-Kohn-Nirenberg inequality ； Hardy inequality ； radial curvature ； Hessian comparison theorem ； sectional curvature