Conservation law of harmonic mappings in supercritical dimensions
Analysis of PDEs
2024-10-15 v1 Differential Geometry
Abstract
In this short note, we provide a partial extension of Rivi\`ere'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.
Keywords
Cite
@article{arxiv.2309.13372,
title = {Conservation law of harmonic mappings in supercritical dimensions},
author = {Chang-Yu Guo and Chang-Lin Xiang},
journal= {arXiv preprint arXiv:2309.13372},
year = {2024}
}
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6 pages