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

Text
10.1007%2Fs11118-014-9427-4 - Published Version Restricted to Repository staff only Download (50kB) |

## 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 |
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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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