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 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Dong, Yuxin Lin, Hezi Lu, Lingen |
| description | 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. |
| doi_str_mv | 10.1007/s00526-024-02688-7 |
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| subjects | 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 |
| title | Sobolev inequalities in manifolds with asymptotically nonnegative curvature |
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