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Research article - Partial differential equations
Conservation law of harmonic mappings in supercritical dimensions
Chang-Yu Guo1; Chang-Lin Xiang2 
1 Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, 266237, Qingdao and Frontiers Science Center for Nonlinear Expectations, Ministry of Education, P. R. China
2 Three Gorges Mathematical Research Center, China Three Gorges University, 443002, Yichang, P. R. China
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 769-773.

In this short note, we provide a partial extension of Rivière’s convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.

Dans cette courte note, nous fournissons une extension partielle de la loi de conservation obtenue par Rivière’s en dimensions supérieures, sous certaines conditions d’intégrabilité de Lorentz pour la matrice de connexion. Comme application, nous obtenons une loi de conservation pour les applications faiblement harmoniques autour de points réguliers en dimensions supercritiques.

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Accepted:
Published online:
DOI: 10.5802/crmath.592
Classification: 58E20, 35J60

Chang-Yu Guo 1; Chang-Lin Xiang 2

1 Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, 266237, Qingdao and Frontiers Science Center for Nonlinear Expectations, Ministry of Education, P. R. China
2 Three Gorges Mathematical Research Center, China Three Gorges University, 443002, Yichang, P. R. China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chang-Yu Guo; Chang-Lin Xiang. Conservation law of harmonic mappings in supercritical dimensions. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 769-773. doi : 10.5802/crmath.592. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.592/

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