Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry
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| Format: | Preprint |
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2024
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| _version_ | 1866914808198070272 |
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| author | Ivanov, Stefan Petkov, Alexander |
| author_facet | Ivanov, Stefan Petkov, Alexander |
| contents | We establish in the present paper two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension $4n+3$, provided some positivity conditions are satisfied. These are qc versions of the prominent Li-Yau gradient estimate in Riemannian geometry. Another goal of this paper is to get two Perelman-type entropy formulas for the qc heat equation on a compact qc-Einstein manifold of dimension $4n+3$ with non-negative qc scalar curvature (e.g. compact $3$-Sasakian manifold), as well as an integral sub-gradient estimate for the positive solutions of the qc heat equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry Ivanov, Stefan Petkov, Alexander Differential Geometry Analysis of PDEs We establish in the present paper two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension $4n+3$, provided some positivity conditions are satisfied. These are qc versions of the prominent Li-Yau gradient estimate in Riemannian geometry. Another goal of this paper is to get two Perelman-type entropy formulas for the qc heat equation on a compact qc-Einstein manifold of dimension $4n+3$ with non-negative qc scalar curvature (e.g. compact $3$-Sasakian manifold), as well as an integral sub-gradient estimate for the positive solutions of the qc heat equation. |
| title | Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2405.14845 |