English

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}
}

Comments

6 pages