The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications

被引：3
作者：
Avalos, R. [1 ]
Freitas, A. [2 ]
机构：
[1] Univ Fed Ceara, Dept Matemat, R Humberto Monte, BR-60455760 Fortaleza, Ceara, Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2021年 / 38卷 / 06期
关键词：
Pohozaev-Schoen identity; Asymptotically Euclidean manifolds; Generalized solitons; Almost-Schur lemma; Static metrics; SCALAR CURVATURE; RICCI; PROOF; FLOW; MASS;
D O I：
10.1016/j.anihpc.2021.01.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically Euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new context. Among these applications, we will show some rigidity results for asymptotically Euclidean Ricci-solitons and Codazzi-solitons. Also, we will present an almost-Schur type inequality valid in this non-compact setting which does not need restrictions on the Ricci curvature. Finally, we will show how some rigidity results related with static potentials also follow from these type of conservation principles. (C) 2021 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.
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页码：1703 / 1724
页数：22
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