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Research articles

ScienceAsia 49 (2023):ID 560-567 |doi: 10.2306/scienceasia1513-1874.2023.011

Gradient estimate for eigenfunctions of the operator on self-shrinkers

Fan-Qi Zeng

ABSTRACT:     In this paper, we study gradient estimates for eigenfunctions associated to the operator L on self-shrinkers. As applications, we obtain a Harnack type inequality concerning those eigenfunctions. Besides, we obtain a gradient estimate of the higher eigenfunctions of the operator L on self-shrinkers.

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a School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000 China

* Corresponding author, E-mail: zengfq@xynu.edu.cn

Received 6 Jul 2022, Accepted 22 Nov 2022