The Caffarelli-Kohn-Nirenberg inequalities and manifolds with nonnegative weighted Ricci curvature

2014/09/19 by Jing Mao, Mao, Jing
Mathematics · Biochemistry, Genetics and Molecular Biology · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Dermatological and Skeletal Disorders

paper · pdf · doi:10.48550/arxiv.1409.5741

Abstract

We prove that n-dimensional (n\geqslant3) complete and non-compact metric measure spaces with non-negative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are close to the model metric measure n-space (i.e., the Euclidean metric n-space).

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