The Caffarelli-kohn-nirenberg Inequalities on Complete Manifolds
نویسندگان
چکیده
We find a new sharp Caffarelli-Kohn-Nirenberg inequality and show that the Euclidean spaces are the only complete non-compact Riemannian manifolds of nonnegative 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.
منابع مشابه
A Caffarelli-Kohn-Nirenberg type inequality on Riemannian manifolds
We establish a generalization to Riemannian manifolds of the Caffarelli-KohnNirenberg inequality. The applied method is based on the use of conformal Killing vector fields and Enzo Mitidieri’s approach to Hardy inequalities. 2000 AMS Mathematics Classification numbers: 58E35, 26D10
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