In this paper, inspired by Brendle (Comm. Pure Appl. Math. 76 (2023), 2192) and Johne (arXiv:2103.08496, 2021), we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry–Émery Ricci curvature.
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Dong et al. (2024) studied this question.
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