Abstract
In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature.
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Supported by the NSFC (11771087, 12171091 and 11831005).
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Dong, Y., Lin, H. & Lu, L. The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature. Acta Math Sci 44, 189–194 (2024). https://doi.org/10.1007/s10473-024-0110-6
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DOI: https://doi.org/10.1007/s10473-024-0110-6