The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications

  • R. Avalos

    Departamento de Matemática, Universidade Federal do Ceará, R. Humberto Monte, 60455-760, Fortaleza, CE, Brazil
  • A. Freitas

    Departamento de Matemática, Universidade Federal da Paraíba, 58059-900, João Pessoa, Paraíba, Brazil
The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications cover

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Abstract

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.

Cite this article

R. Avalos, A. Freitas, The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 6, pp. 1703–1724

DOI 10.1016/J.ANIHPC.2021.01.002