Gradient estimates for $Δ_b u + au^{p+1} = 0$ on pseudo-Hermitian manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909297443602432 |
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| author | Zhao, Biqiang |
| author_facet | Zhao, Biqiang |
| contents | In this paper, we derive the gradient estimates for the positive solutions of the equation $Δ_b u + au^{p+1} = 0$ on complete noncompact pseudo-Hermitian manifolds, where $a > 0$ and $p \leq 0$ or $a < 0$ and $p > 0$ are two constants. As an application, we will obtain a Liouville-type theorem when the manifolds are Sasakian-type with nonnegative pseudo-Hermitian Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for $Δ_b u + au^{p+1} = 0$ on pseudo-Hermitian manifolds Zhao, Biqiang Differential Geometry In this paper, we derive the gradient estimates for the positive solutions of the equation $Δ_b u + au^{p+1} = 0$ on complete noncompact pseudo-Hermitian manifolds, where $a > 0$ and $p \leq 0$ or $a < 0$ and $p > 0$ are two constants. As an application, we will obtain a Liouville-type theorem when the manifolds are Sasakian-type with nonnegative pseudo-Hermitian Ricci curvature. |
| title | Gradient estimates for $Δ_b u + au^{p+1} = 0$ on pseudo-Hermitian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.14920 |