Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications
Autor: | Zhao, Guangwen |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: This version revises the statements of Corollary 1.2 and Corollary 1.6 in the version dated April 16, 2024, making them clearer, and also corrects some typographical errors |
Databáze: | arXiv |
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