Rigidity of the subelliptic heat kernel on $\operatorname{SU}(2)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916560432529408 |
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| author | Gordina, Maria Wang, Jing |
| author_facet | Gordina, Maria Wang, Jing |
| contents | We study heat kernel rigidity for the Lie group $\operatorname{SU}\left( 2 \right)$ kernel equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to the Hopf fibration $\operatorname{U}\left( 1 \right)\to \operatorname{SU}\left( 2 \right)\to \mathbb{CP}^1$, which coincides with the sub-Riemannian sphere $\operatorname{SU}\left( 2 \right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of the subelliptic heat kernel on $\operatorname{SU}(2)$ Gordina, Maria Wang, Jing Analysis of PDEs Probability We study heat kernel rigidity for the Lie group $\operatorname{SU}\left( 2 \right)$ kernel equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to the Hopf fibration $\operatorname{U}\left( 1 \right)\to \operatorname{SU}\left( 2 \right)\to \mathbb{CP}^1$, which coincides with the sub-Riemannian sphere $\operatorname{SU}\left( 2 \right)$. |
| title | Rigidity of the subelliptic heat kernel on $\operatorname{SU}(2)$ |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2407.12183 |