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arXiv · 2404.10417

Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications

Guangwen Zhao
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Abstract

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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Guangwen Zhao. 2024-04-16. Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications. https://arxiv.org/abs/2404.10417

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