Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909192112046080 |
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| author | Zhao, Guangwen |
| author_facet | Zhao, Guangwen |
| contents | We prove a local gradient estimate for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons given by a general conformal vector field. As an application, we obtain a Liouville type theorem for $ \mathcal{L} u = 0 $, which improves the one of Li--Sun (Acta Math. Sin. (Engl. Ser.), 37(11): 1768--1782, 2021.). We also consider applications where manifolds are special conformal solitons. Especially in the case of self-shrinkers, a better Liouville type theorem is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications Zhao, Guangwen Differential Geometry We prove a local gradient estimate for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons given by a general conformal vector field. As an application, we obtain a Liouville type theorem for $ \mathcal{L} u = 0 $, which improves the one of Li--Sun (Acta Math. Sin. (Engl. Ser.), 37(11): 1768--1782, 2021.). We also consider applications where manifolds are special conformal solitons. Especially in the case of self-shrinkers, a better Liouville type theorem is obtained. |
| title | Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.10417 |