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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.
Keywords: Pohozaev-Schoen identity, Asymptotically Euclidean manifolds, Generalized solitons, Almost-Schur lemma, Static metrics
Avalos, R. 1 ; Freitas, A. 2
@article{AIHPC_2021__38_6_1703_0,
author = {Avalos, R. and Freitas, A.},
title = {The {Pohozaev-Schoen} identity on asymptotically {Euclidean} manifolds: {Conservation} laws and their applications},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1703--1724},
publisher = {Elsevier},
volume = {38},
number = {6},
year = {2021},
doi = {10.1016/j.anihpc.2021.01.002},
mrnumber = {4327894},
zbl = {1483.53058},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2021.01.002/}
}
TY - JOUR AU - Avalos, R. AU - Freitas, A. TI - The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 2021 SP - 1703 EP - 1724 VL - 38 IS - 6 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2021.01.002/ DO - 10.1016/j.anihpc.2021.01.002 LA - en ID - AIHPC_2021__38_6_1703_0 ER -
%0 Journal Article %A Avalos, R. %A Freitas, A. %T The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications %J Annales de l'I.H.P. Analyse non linéaire %D 2021 %P 1703-1724 %V 38 %N 6 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2021.01.002/ %R 10.1016/j.anihpc.2021.01.002 %G en %F AIHPC_2021__38_6_1703_0
Avalos, R.; Freitas, A. The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1703-1724. doi: 10.1016/j.anihpc.2021.01.002
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