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

Text s11118-014-9427-4.pdf - Published Version Restricted to Repository staff only Download (338kB)

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).

Actions (login required)

Edit Item