Barbosa, Ezequiel and Kristály, Alexandru (2017) Secondorder Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. ISSN 00246093 (In Press)

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Abstract
Let (M, g) be an n−dimensional complete open Riemannian manifold with nonnegative Ricci curvature verifying ρ∆gρ ≥ n − 5 ≥ 0, where ∆g is the LaplaceBeltrami operator on (M, g) and ρ is the distance function from a given point. If (M, g) supports a secondorder Sobolev inequality with a constant C > 0 close to the optimal constant K0 in the secondorder Sobolev inequality in R n , we show that a global volume noncollapsing property holds on (M, g). The latter property together with a Perelmantype construction established by Munn (J. Geom. Anal., 2010) provide several rigidity results in terms of the higherorder homotopy groups of (M, g). Furthermore, it turns out that (M, g) supports the secondorder Sobolev inequality with the constant C = K0 if and only if (M, g) is isometric to the Euclidean space R n .
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis 
Depositing User:  Dr. Alexandru Kristaly 
Date Deposited:  07 Nov 2017 08:46 
Last Modified:  07 Nov 2017 08:46 
URI:  http://real.mtak.hu/id/eprint/67173 
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