This volume offers an expanded version of lectures given at the Courant Institute on the
theory of Sobolev spaces on Riemannian manifolds.``Several surprising phenomena …

These notes form a summary of a mini-course given at the Eidgenossische Technische
Hochschule in Zurich in November 1998. They aim to present some of the basic ideas in the …

By using optimal mass transport theory we prove a sharp isoperimetric inequality in CD (0,
N) metric measure spaces assuming an asymptotic volume growth at infinity. Our result …

We present a rigidity scenario for complete Riemannian manifolds supporting the
Heisenberg–Pauli–Weyl uncertainty principle with the sharp constant in R n (shortly, sharp …

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 …

The Gagliardo–Nirenberg inequalities and manifolds of non-negative Ricci curvature Page 1
Journal of Functional Analysis 224 (2005) 230–241 www.elsevier.com/locate/jfa The …

By the method of optimal mass transport we prove a sharp isoperimetric inequality in CD (0,
N) metric measure spaces involving the asymptotic volume ratio at infinity, N> 1. In the …

Let (M, g) be a smooth compact Riemannian manifold, and G a subgroup of the isometry
group of (M, g). We compute the value of the best constant in Sobolev inequalities when the …

The best-constant problem for Nash and Sobolev inequalities on Riemannian manifolds has
been intensively studied in the last few decades, especially in the compact case. We treat …

Let (M, g) be a compact Riemannian manifold of dimension n≥ 2 and 1< p≤ 2. In this work
we prove the validity of the optimal Gagliardo–Nirenberg inequality\left (\,\int_M| u|^ r …