Gradient Estimates for the Positive Solutions of $$\mathfrak {L}u=0$$ on Self-Shrinkers |
| |
Authors: | Email author" target="_blank">Yecheng?ZhuEmail author Qing?Chen |
| |
Institution: | 1.Department of Mathematics,University of Science and Technology of China,Hefei,People’s Republic of China;2.Department of Applied Mathematics,Anhui University of Technology,Maanshan,People’s Republic of China |
| |
Abstract: | In this paper, we investigate the positive solutions of \(\mathfrak {L}u=0\) on a self-shrinker. First, we prove a global gradient estimate for the positive solutions, and obtain a strong Liouville theorem. Then by the generalized Laplacian comparison theorem for the distance function on a self-shrinker, we derive a local gradient estimate for the positive solutions. At last, we collect some applications of the local gradient estimate for the positive solutions on self-shrinkers. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|