The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: conservation laws and their applications (Q2235187)

The main purposes of the paper under review are two: (1) to present a Pohozaev-Schoen identity on Asymptotically Euclidean (AE) manifolds and (2) to apply this result to obtain rigidity theorems in the case of AE generalized solitons (Ricci-solitons and Codazzi-solitons), to obtain a generalized almost-Schur-type inequality, and to prove some identities related with rigidity of static potentials on AE manifolds. The paper is in the spirit of the papers of \textit{E. Barbosa} [Proc. Am. Math. Soc. 140, No. 12, 4319--4322 (2012; Zbl 1273.53042)] and \textit{E. Barbosa} et al. [Commun. Anal. Geom. 28, No. 2, 223--242 (2020; Zbl 1441.53035)]. Although the paper is very technical, it is very well written and motivated.