Conservation law of harmonic mappings in supercritical dimensions
Chang-Yu Guo, Chang-Lin Xiang
TL;DR
This paper extends Rivi e's conservation law to higher dimensions under Lorentz integrability conditions, providing a new conservation law for weakly harmonic mappings in supercritical dimensions.
Contribution
It offers a partial extension of Rivi e's conservation law to supercritical dimensions with Lorentz integrability assumptions.
Findings
Conservation law extended to higher dimensions.
Applicable to weakly harmonic mappings.
Under Lorentz integrability conditions.
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.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons