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This document presents a study of the Caffarelli-Kohn-Nirenberg (CKN) inequality for submanifolds in Riemannian manifolds. It begins with preliminaries on submanifolds and integral inequalities. It then proves the Hardy, weighted Sobolev, and CKN inequalities for submanifolds in manifolds where the radial sectional curvature is bounded above by a function K. Examples are given of manifolds satisfying this curvature condition, including Cartan-Hadamard manifolds.

Author

Music Connection Narva

Language

EN