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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.

58E20 Harmonic maps, etc.
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI
[1] Freed D. S., J. Diff. Geom. 28 pp 223– (1988)
[2] DOI: 10.1002/cpa.3160330604 · Zbl 0475.58005 · doi:10.1002/cpa.3160330604
[3] DOI: 10.1016/0003-4916(82)90077-X · Zbl 0512.58018 · doi:10.1016/0003-4916(82)90077-X
[4] DOI: 10.1002/cpa.3160410405 · Zbl 0686.35081 · doi:10.1002/cpa.3160410405
[5] DOI: 10.1002/cpa.3160420102 · Zbl 0685.58016 · doi:10.1002/cpa.3160420102
[6] DOI: 10.1007/BF02415020 · Zbl 0328.34055 · doi:10.1007/BF02415020
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