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The aim of this paper is to present a version of the generalizedPohozaev-Schoen identity in the context of asymptotically euclidean manifolds.Since these kind of geometric identities have proven to be a very powerful toolwhen analysing different geometric problems for compact manifolds, we willpresent a variety of applications within this new context. Among theseapplications, we will show some rigidity results for asymptotically euclideanRicci-solitons and Codazzi-solitons. Also, we will present an almost-Schur-typeinequality valid in this non-compact setting which does not need restrictionson the Ricci curvature. Finally, we will show how some rigidity results relatedwith static potentials also follow from these type of conservation principles.

The Pohozaev-Schoen Identity on Asymptotically Euclidean Manifolds: Conservation Identities and their applications