Sobolev inequalities in manifolds with asymptotically nonnegative curvature

Using the ABP-method as in a recent work by Brendle (Commun Pure Appl Math 76:2192–2218, 2022), we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian manifold with asymptotically nonnegative Ricci/sectional curvature. These inequ...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2024-05, Vol.63 (4), Article 110
Hauptverfasser:	Dong, Yuxin, Lin, Hezi, Lu, Lingen
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Asymptotic properties Calculus of Variations and Optimal Control Optimization Control Curvature Inequalities Manifolds (mathematics) Mathematical and Computational Physics Mathematics Mathematics and Statistics Riemann manifold Systems Theory Theoretical
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Zusammenfassung:	Using the ABP-method as in a recent work by Brendle (Commun Pure Appl Math 76:2192–2218, 2022), we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian manifold with asymptotically nonnegative Ricci/sectional curvature. These inequalities generalize those given by Brendle in the case of complete Riemannian manifolds with nonnegative curvature.
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-024-02688-7