Complete manifolds with non-negative Ricci curvature and the Caffarelli–Kohn–Nirenberg inequalities

By M. Carmo, C. Xia. Compositio Mathematica, 2004

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Hardy inequalities on Riemannian manifolds and applications (2012, background): “On the other hand, the knowledge of the best constants for the inequalities plays a crucial role in [2,14,50].”
Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature (2020, background): “Moreover, a quantitative form of Ledoux’s result were given by do Carmo and Xia [24] who proved that (M,g) is topologically close to (Rn, g0) whenever the constant C > AT(n, p) in (S) is sufficiently close to AT(n, p).”
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “2 can be included into the best constant program initiated by Aubin [4], and studied by Ledoux [30], Cheeger and Colding [12], Druet, Hebey and Vaugon [16], do Carmo and Xia [15], Minerbe [32], Li and Wang [31], etc.”
Improved Hardy and Rellich inequalities on Riemannian manifolds (2007, background): “Similarly, in [19], [20], [9], geometric properties such as volume growth and isoperimetric proﬁle are related to the existence of Hardy type inequalities.”