The Yamabe flow on asymptotically flat manifolds

被引：1

作者：

Chen, Eric ^{[1
]}

Wang, Yi ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 803期

关键词：

CONVERGENCE; MASS; EXISTENCE; EQUATIONS;

D O I：

10.1515/crelle-2023-0052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Yamabe flow starting from an asymptotically flat manifold ( M-n , g(0) ). We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if Y(M, [g(0)] ) > 0, and show that the flow does not converge otherwise. If the scalar curvature is nonnegative and integrable, then the ADM mass at time infinity drops by the limit of the total scalar curvature along the flow.

引用

页码：61 / 101

页数：41

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