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- Title
Sobolev inequalities in manifolds with asymptotically nonnegative curvature.
- Authors
Dong, Yuxin; Lin, Hezi; Lu, Lingen
- Abstract
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.
- Subjects
ISOPERIMETRIC inequalities; RIEMANNIAN manifolds; CURVATURE; SUBMANIFOLDS; MATHEMATICS
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-024-02688-7