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On harmonic maps into gauge groups. (English) Zbl 0934.58017
Summary: We continue the work of the paper [Q. Ding and B. Lu, J. Math. Phys. 37, No. 8, 4076-4088 (1996; Zbl 0871.58024)] on the existence of globally defined harmonic maps from the Minkowski plane \(R^{1,1}\) into an infinite-dimensional Hilbert Lie group. We prove that the Cauchy problem for harmonic maps from \(R^{1,1}\) into Hilbert loop groups \(H_s(LG)\) can be solved globally for all remaining cases \({1\over 2}< s\leq{3\over 4}\) and we obtain similar results for harmonic maps from \(R^{1,1}\) into certain Hilbert Lie gauge groups \(H_s(S^n, G)\) \((n\geq 2)\). These answer the two questions remaining from the above paper.
MSC:
58E20 Harmonic maps, etc.
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
22E67 Loop groups and related constructions, group-theoretic treatment
53C20 Global Riemannian geometry, including pinching
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