Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications
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.)...
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| Format: | Journal Article |
| Language: | English |
| Published: |
16-04-2024
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | 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. |
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| DOI: | 10.48550/arxiv.2404.10417 |