@article {
author = {Hajiaghasi, Sakineh and Azami, Shahroud},
title = {A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons},
journal = {Sahand Communications in Mathematical Analysis},
volume = {},
number = {},
pages = {-},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1972568.1199},
abstract = {In this paper, we consider positive solutions for the Allen-Cahn equation\begin{equation*}\Delta u+\left(1-u^{2}\right)u=0,\end{equation*}on an almost Ricci soliton without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality, we estimate the upper bound of $\vert \nabla u\vert^{2}$. As one of the applications, we extend this result to a gradient Ricci almost soliton. Finally, we obtain a Liouville-type theorem for almost Ricci solitons.},
keywords = {Gradient estimate,Almost Ricci soliton,Allen-Cahn equation},
url = {https://scma.maragheh.ac.ir/article_706806.html},
eprint = {}
}