Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2311.01063 |
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Sommario:
- We use maximum principle to prove the Liouville theorem of the equation $ΔU + b\cdot \nabla U + h U^α = 0, U \geq 0, 0 < α< \frac{n + 2}{n - 2}$ on the complete Riemannian manifold with non-negative Ricci tensor, which improve the result of Gidas-Spruck and Catino-Monticelli. We remark that this is the second version and all of the results come from the first version. Two months after we posted version 1 of this preprint on arXiv, we found Zhihao Lu has already posted a paper arXiv:2308.14764 before us and part of his result coincides with ours. So after deleting these parts and adding more reference and details, we post this second version on arXiv.