The Gagliardo–Nirenberg inequalities and manifolds of non-negative Ricci curvature

This article is devoted to show that complete non-compact Riemannian manifolds with nonnegative Ricci curvature of dimension greater than or equal to two in which some Gagliardo– Nirenberg type inequality holds are not very far from the Euclidean space. © 2004 Elsevier Inc. All rights reserved.