| Tartalmi leírás: |
Two Morrey-Sobolev inequalities (with support-bound and L 1?bound, respectively) are investigated on complete Riemannian manifolds with their sharp constants in ? 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 ? 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 ? n , e).
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