GEOMETRIC INEQUALITIES AND RIGIDITY OF GRADIENT SHRINKING RICCI SOLITONS

被引：0
作者：
Wu, Jia-Yong [1 ,2 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China
来源：
ASIAN JOURNAL OF MATHEMATICS | 2024年 / 28卷 / 05期
关键词：
shrinking Ricci soliton; Schrodinger operator; Sobolev inequality; logarithmic Sobolev inequality; heat kernel; Faber-Krahn inequality; Nash inequality; Rozenblum-Cwikel-Lieb inequality; eigenvalue; half Weyl tensor; rigidity; SOBOLEV INEQUALITIES; COMPACTNESS THEOREM; HEAT-EQUATION; MANIFOLDS; CLASSIFICATION; 4-MANIFOLDS; CURVATURE; CONSTANTS; BOUNDS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schrodinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and the Rozenblum-Cwikel-Lieb inequality all equivalently exist on complete gradient shrinking Ricci solitons. We also obtain some integral gap theorems for compact shrinking Ricci solitons.
引用
收藏
页码：549 / 580
页数：32
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