Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold

Jiayu Li; Lei Liu

doi:10.2140/pjm.2019.299.33

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arXiv · 1704.08673

Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold

Jiayu Li·Lei Liu

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Abstract

In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain $\Omega\subset\R^m$ to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose $(m-2)$-dimension Hausdorff measure is zero. Moreover, if the target manifold $N$ does not admit any harmonic sphere $S^l$, $l=2,...,m-1$, we will show $(u,v)$ is smooth.

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Jiayu Li, Lei Liu. 2017-04-27. Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold. https://doi.org/10.2140/pjm.2019.299.33

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