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Abstract
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We study the partial regularity theorem for stationary harmonic maps from a
Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map
from a smooth
bounded open domain
to a Lorentzian manifold with Dirichlet boundary condition,
we prove that it is smooth outside a closed set whose
-dimensional
Hausdorff measure is zero. Moreover, if the target manifold
does not admit any
harmonic spheres
,
, we
show
is
smooth.
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Keywords
Lorentzian harmonic map, stationary, partial regularity,
blow-up
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Mathematical Subject Classification 2010
Primary: 53C43, 58E20
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Milestones
Received: 4 August 2017
Revised: 15 May 2018
Accepted: 24 June 2018
Published: 18 April 2019
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