Mathematical Research Letters

Volume 14 (2007)

Number 5

The Caffarelli-Kohn-Nirenberg Inequalities on Complete Manifolds

Pages: 875 – 885



Changyu Xia (Universidade de Brasília)


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.

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