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

Published online by Cambridge University Press:  04 December 2007

Manfredo Perdigão do Carmo  and
Changyu Xia
Manfredo Perdigão do Carmo
Affiliation:
Institute de Matematica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botanico, 22460-320 Rio de Janeiro RJ, [email protected]
Changyu Xia
Affiliation:
Departamento de Matemática-IE, Fundação Universidade de Brasília, Campus Universitário, 70910-900 Brasília DF, [email protected]
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Abstract

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In this paper, we prove that complete open Riemannian manifolds with non-negative Ricci curvature of dimension greater than or equal to three in which some Caffarelli–Kohn–Nirenberg type inequalities are satisfied are close to the Euclidean space.

Keywords

manifoldsRicci curvatureSobolev inequalities53C2053C2157R7031C12
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 818 - 826
Copyright
Foundation Compositio Mathematica 2004