Barbosa, E. & Kristály, A. (2018) Bulletin of the London Mathematical Society [Matematică, Q1]

Publicat: 24 Noiembrie 2020

Barbosa, E. & Kristály, A. (2018) Second‐order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature. Bulletin of the London Mathematical Society, 50(1), 35-45.

DOI: https://doi.org/10.1112/blms.12107

✓ Publisher: Wiley
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.077 (2018) / Q1

Abstract: Let (M,g) be an n-dimensional complete open Riemannian manifold with nonnegative Ricci curvature verifying gn-50, where g is the Laplace-Beltrami operator on (M,g) and is the distance function from a given point. If (M,g) supports a second-order Sobolev inequality with a constant C>0 close to the optimal constant K0 in the second-order Sobolev inequality in Rn, we show that a global volume noncollapsing property holds on (M,g). The latter property together with a Perelman-type construction established by Munn (J. Geom. Anal. (2010) 723-750) provide several rigidity results in terms of the higher order homotopy groups of (M,g). Furthermore, it turns out that (M,g) supports the second-order Sobolev inequality with the constant C=K0 if and only if (M,g) is isometric to the Euclidean space Rn.

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