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On harmonic maps from $$R^{1,1}$$ into Hilbert loop groups. (English) Zbl 0871.58024
Let $$H_s(LG)=\{\gamma:S^1\to G\mid \gamma$$ is $$H_s$$ integrable} $$(s>\frac12)$$ be the real Hilbert loop group of a compact Lie group. The authors prove that the Cauchy problem for harmonic maps from the Minkowski plane $$\mathbb{R}^{1,1}$$ into Hilbert loop groups $$H_s(LG)$$ exists globally and uniquely when $$s>\frac34$$. The construction of the harmonic maps strongly depends on some geometric properties of the loop groups.

##### MSC:
 58E20 Harmonic maps, etc. 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
##### Keywords:
Minkowski space; Hilbert loop group; harmonic maps
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##### References:
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