Mathematical Research Letters
Volume 14 (2007)
The Caffarelli-Kohn-Nirenberg Inequalities on Complete Manifolds
Pages: 875 – 885
We find a new sharp Caffarelli-Kohn-Nirenberg inequality and show that the Euclidean spaces are the only complete non-compact Riemannian manifolds of non-negative Ricci curvature satisfying this inequality. We also show that a complete open manifold with non-negative Ricci curvature in which the optimal Nash inequality holds is isometric to a Euclidean space.