REAL

Sharp Morrey-Sobolev Inequalities on Complete Riemannian Manifolds

Kristály, Alexandru (2015) Sharp Morrey-Sobolev Inequalities on Complete Riemannian Manifolds. Potential Analysis, 42 (1). pp. 141-154. ISSN 0926-2601

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10.1007%2Fs11118-014-9427-4 - Published Version
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Abstract

Two Morrey-Sobolev inequalities (with support-bound and L 1−bound, respectively) are investigated on complete Riemannian manifolds with their sharp constants in ℝ n . We prove the following results in both cases: If (M, g) is a Cartan-Hadamard manifold which verifies the n−dimensional Cartan-Hadamard conjecture, sharp Morrey-Sobolev inequalities hold on (M, g). Moreover, extremals exist if and only if (M, g) is isometric to the standard Euclidean space ℝ n , e). If (M, g) has non-negative Ricci curvature, (M, g) supports the sharp Morrey-Sobolev inequalities if and only if (M, g) is isometric to ℝ n , e).

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria
Depositing User: Dr. Alexandru Kristaly
Date Deposited: 09 Sep 2015 08:15
Last Modified: 09 Sep 2015 08:15
URI: http://real.mtak.hu/id/eprint/26094

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