Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912870359367680 |
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| author | Lu, Lingen |
| author_facet | Lu, Lingen |
| contents | In this paper, we employ the ABP method developed by Brendle to establish the optimal $L^p$ logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp $L^2$ logarithmic Sobolev inequality for submanifolds in manifolds with nonnegative sectional curvature. The sharp constants in both inequalities depend on the asymptotic volume ratio of the ambient manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17748 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method Lu, Lingen Differential Geometry Analysis of PDEs In this paper, we employ the ABP method developed by Brendle to establish the optimal $L^p$ logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp $L^2$ logarithmic Sobolev inequality for submanifolds in manifolds with nonnegative sectional curvature. The sharp constants in both inequalities depend on the asymptotic volume ratio of the ambient manifold. |
| title | Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2601.17748 |