A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons

被引：0

作者：

Hajiaghasi, Sakineh ^{[1
]}

Azami, Shahroud ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Fac Sci, Dept Pure Math, Qazvin, Iran

来源：

SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS | 2024年 / 21卷 / 01期

关键词：

Gradient estimate; Almost Ricci soliton; Allen-Cahn equa-tion; LIOUVILLE THEOREM; MANIFOLDS; CURVATURE; KERNEL; SCHEME;

D O I：

10.22130/scma.2023.1972568.1199

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider positive solutions for the Allen-Cahn equation triangle u + (1 - u(2)) u = 0, on an almost Ricci soliton without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality, we estimate the upper bound of |del u|(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.

引用

页码：83 / 98

页数：17