Shannon's inequality on non-collapsing RCD spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916471494410240 |
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| author | Kitabeppu, Yu |
| author_facet | Kitabeppu, Yu |
| contents | We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel. Also we have a cone rigidity result. As an application, we have the so-called uncertainty principle inequality on such spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shannon's inequality on non-collapsing RCD spaces Kitabeppu, Yu Metric Geometry We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel. Also we have a cone rigidity result. As an application, we have the so-called uncertainty principle inequality on such spaces. |
| title | Shannon's inequality on non-collapsing RCD spaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2404.06719 |