Sobolev inequality on manifolds with asymptotically nonnegative Bakry-Émery Ricci curvature. (English) Zbl 1543.35008
Summary[: In this paper, inspired by S. Brendle [Commun. Pure Appl. Math. 76, No. 9, 2192–2218 (2023; Zbl 1527.53030)] and F. Johne [“Sobolev inequalities on manifolds with nonnegative Bakry-Émery Ricci curvature”, Preprint, arXiv:2103.08496], we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry-Émery Ricci curvature.
© 2024 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
© 2024 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
MSC:
| 35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Citations:
Zbl 1527.53030References:
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