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

Autor:	Zhao, Guangwen
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry
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
Externí odkaz:	http://arxiv.org/abs/2404.10417 Zobrazit plný text záznamu View this record from Arxiv