Perelman's entropy and heat kernel bounds on RCD spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910859168579584 |
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| author | Brena, Camillo |
| author_facet | Brena, Camillo |
| contents | We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-Émery Ricci curvature bounded from below. We rigorously justify the formula for the time derivative of the W-entropy and derive its monotonicity and rigidity properties. Additionally, we establish bounds for solutions of the heat equation, which are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perelman's entropy and heat kernel bounds on RCD spaces Brena, Camillo Differential Geometry We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-Émery Ricci curvature bounded from below. We rigorously justify the formula for the time derivative of the W-entropy and derive its monotonicity and rigidity properties. Additionally, we establish bounds for solutions of the heat equation, which are of independent interest. |
| title | Perelman's entropy and heat kernel bounds on RCD spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.03017 |