Vol. 299, No. 1, 2019

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

Jiayu Li and Lei Liu

Vol. 299 (2019), No. 1, 33–52
Abstract

We 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 Ω m to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose (m2)-dimensional Hausdorff measure is zero. Moreover, if the target manifold N does not admit any harmonic spheres Sl , l = 2,,m 1, we show (u,v) is smooth.

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Keywords
Lorentzian harmonic map, stationary, partial regularity, blow-up
Mathematical Subject Classification 2010
Primary: 53C43, 58E20
Milestones
Received: 4 August 2017
Revised: 15 May 2018
Accepted: 24 June 2018
Published: 18 April 2019
Authors
Jiayu Li
School of Mathematical Sciences
University of Science and Technology of China
Hefei
China
Lei Liu
Max Planck Institute for Mathematics in the Sciences
Leipzig
Germany