The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications |
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| Affiliation: | 1. Departamento de Matemática, Universidade Federal do Ceará, R. Humberto Monte, 60455-760, Fortaleza, CE, Brazil;2. Departamento de Matemática, Universidade Federal da Paraíba, 58059-900, João Pessoa, Paraíba, Brazil;1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;2. School of Mathematical Sciences, Peking University, 100871, Beijing, China;1. CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, PSL Research University, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France;2. CMLS, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France;1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic;2. Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany;3. Université de Toulon, IMATH, EA 2134, BP 20132, 83957 La Garde, France;1. Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada;2. School of mathematical sciences, University of Chinese academy of sciences, Beijing, China |
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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. |
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| Keywords: | Pohozaev-Schoen identity Asymptotically Euclidean manifolds Generalized solitons Almost-Schur lemma Static metrics |
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