Abstract
We prove a sharp Log-Sobolev inequality for submanifolds of a complete non-compact Riemannian manifold with asymptotic non-negative intermediate Ricci curvature and Euclidean volume growth. Our work extends a result of Dong et al. (Acta Math. Sci. Ser. B (Engl. Ed.), 44(1):189–194 (2024)) which already generalizes Yi and Zheng (To appear in Chin. Ann. Math., (2023)) and Brendle (Comm. Pure Appl. Math. 75(3), 449–454 (2022)).
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