Probability Versions of Li-Yau Type Inequalities and Applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910686657904640 |
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| author | Wang, Feng-Yu Cheng, Li-Juan |
| author_facet | Wang, Feng-Yu Cheng, Li-Juan |
| contents | By using stochastic analysis, two probability versions of Li-Yau type inequalities are established for diffusion semigroups on a manifold possibly with (non-convex) boundary. The inequalities are explicitly given by the Bakry-Emery curvature-dimension, as well as the lower bound of the second fundamental form if the boundary exists. As applications, a number of global and local estimates are presented, which extend or improve existing ones derived for manifolds without boundary. Compared with the maximum principle technique developed in the literature, the probabilistic argument we used is more straightforward and hence considerably simpler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probability Versions of Li-Yau Type Inequalities and Applications Wang, Feng-Yu Cheng, Li-Juan Probability Differential Geometry 58J65, 60H30 By using stochastic analysis, two probability versions of Li-Yau type inequalities are established for diffusion semigroups on a manifold possibly with (non-convex) boundary. The inequalities are explicitly given by the Bakry-Emery curvature-dimension, as well as the lower bound of the second fundamental form if the boundary exists. As applications, a number of global and local estimates are presented, which extend or improve existing ones derived for manifolds without boundary. Compared with the maximum principle technique developed in the literature, the probabilistic argument we used is more straightforward and hence considerably simpler. |
| title | Probability Versions of Li-Yau Type Inequalities and Applications |
| topic | Probability Differential Geometry 58J65, 60H30 |
| url | https://arxiv.org/abs/2411.03712 |