A Liouville theorem for the CR Yamabe type equation on Sasakian manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917438050795520 |
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| author | Zhao, Biqiang |
| author_facet | Zhao, Biqiang |
| contents | In this paper, we study the CR Yamabe type equation \begin{align}
Δ_b u+F(u)=0 \nonumber
\end{align} on complete noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. Under some assumptions, we prove a rigidity result, that is, the manifold is CR isometric to Heisenberg group $\mathbb{H}^n$. The proofs are based on the Jerison-Lee's differential identity combining with integral estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Liouville theorem for the CR Yamabe type equation on Sasakian manifolds Zhao, Biqiang Differential Geometry Analysis of PDEs In this paper, we study the CR Yamabe type equation \begin{align} Δ_b u+F(u)=0 \nonumber \end{align} on complete noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. Under some assumptions, we prove a rigidity result, that is, the manifold is CR isometric to Heisenberg group $\mathbb{H}^n$. The proofs are based on the Jerison-Lee's differential identity combining with integral estimates. |
| title | A Liouville theorem for the CR Yamabe type equation on Sasakian manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.06779 |