渐近欧氏流形上的Pohozaev-Schoen恒等式：守恒恒等式及其应用
The Pohozaev-Schoen Identity on Asymptotically Euclidean Manifolds: Conservation Identities and their applications
摘要：
本文的目的是提出一个版本的广义Pohozaev-Schoen恒等式的上下文中的渐近欧氏流形。由于这种几何恒等式已被证明是一个非常强大的工具，当分析不同的几何问题的紧流形，我们将提出各种应用在这个新的背景下。在这些应用中，我们将给出渐近欧氏Ricci孤子和Codazzi孤子的刚性结果。另外，我们还提出了一个在这种非紧情形下有效的几乎Schur型不等式，它不需要对里奇曲率进行限制.最后，我们将展示一些与静电势相关的刚性结果如何也遵循这些类型的守恒原理。
英文摘要：
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.
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