The Caffarelli-Kohn-Nirenberg Inequalities on Complete Manifolds

• Autores: Changyu Xia
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 5, 2007, págs. 875-885
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n5.a14
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• Resumen

  • 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