论文标题
渐近欧几里得$ q $ singular空间的刚性定理
Rigidity Theorems for Asymptotically Euclidean $Q$-singular Spaces
论文作者
论文摘要
在本文中，我们证明了一些与$ q $ c左右分析有关的僵化定理，这些分析是尤克里德人（AE）流形的，这些分析的灵感来自第四阶重力理论中保护原理的分析。该分析中的一个中心对象是第四阶能量的概念，该阶先前由作者进行了分析，该概述符合正能定理。我们表明，这种能量可以通过与Ricci Tensor的第四阶类似物来更加几何地重写，我们用$ j_g $表示。这使我们能够证明Yamabe阳性$ J $ -FLAT AE歧管必须等于欧几里得空间。作为产品，我们证明了这种$ j $ -tensor为无穷大的最佳衰减率提供了几何控制。最后的结果加强了$ j $的类比，作为与Ricci张量的第四阶类似物。
In this paper we prove some rigidity theorems associated to $Q$-curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation principles within fourth order gravitational theories. A central object in this analysis is a notion of fourth order energy, previously analysed by the authors, which is subject to a positive energy theorem. We show that this energy can be more geometrically rewritten in terms of a fourth order analogue to the Ricci tensor, which we denote by $J_g$. This allows us to prove that Yamabe positive $J$-flat AE manifolds must be isometric to Euclidean space. As a by product, we prove that this $J$-tensor provides a geometric control for the optimal decay rates at infinity. This last result reinforces the analogy of $J$ as a fourth order analogue to the Ricci tensor.
