论文标题
在渐近欧几里得歧管上的pohozaev-schoen身份：保护身份及其应用
The Pohozaev-Schoen Identity on Asymptotically Euclidean Manifolds: Conservation Identities and their applications
论文作者
论文摘要
本文的目的是在渐近的欧几里得流形的背景下介绍广义的Pohozaev-Schoen身份。由于在分析针对紧凑型歧管的不同几何问题时，事实证明，这类几何身份已被证明是一种非常强大的工具，因此我们将在这种新环境中介绍各种应用程序。在这些应用中，我们将对渐近的欧几里得ricci-Solitons和Codazzi-Solitons显示一些刚性结果。另外，我们将提出在这种非紧凑型环境中有效的几乎距离类型的不平等，该设置不需要对RICCI曲率限制。最后，我们将展示与这些类型的保护原则有关的一些与静态电位相关的刚度结果。
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.
