A positive energy theorem for fourth-order gravity

被引：0
作者：
Rodrigo Avalos
Paul Laurain
Jorge H. Lira
机构：
[1] Federal University of Ceará,Mathematics Department
[2] Université de Paris,Institut Mathématique de Jussieu
[3] PSL Research University,DMA, Ecole normale supérieure, CNRS
来源：
Calculus of Variations and Partial Differential Equations | 2022年 / 61卷
关键词：
35R01; 53A30;
D O I：
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摘要：
In this paper we prove a positive energy theorem related to fourth-order gravitational theories, which is a higher-order analogue of the classical ADM positive energy theorem of general relativity. We will also show that, in parallel to the corresponding situation in general relativity, this result intersects several important problems in geometric analysis. For instance, it underlies positive mass theorems associated to the Paneitz operator, playing a similar role in the positive Q-curvature conformal prescription problem as the Schoen–Yau positive energy theorem does for the Yamabe problem. Several other links to Q-curvature analysis and rigidity phenomena are established.
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