Gu, Chaohao On the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space. (English) Zbl 0475.58005 Commun. Pure Appl. Math. 33, 727-737 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 51 Documents MSC: 58E20 Harmonic maps, etc. 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 81T08 Constructive quantum field theory 35Q99 Partial differential equations of mathematical physics and other areas of application 58J90 Applications of PDEs on manifolds Keywords:harmonic map between pseudo-Riemannian manifolds; extremal of the energy functional; chiral fields; maps from 2-dimensional Minkowski space to complete Riemannian manifold; Cauchy problem; harmonic maps into the sphere; Sine-Gordon equation; sigma-models Citations:Zbl 0401.58003 PDFBibTeX XMLCite \textit{C. Gu}, Commun. Pure Appl. Math. 33, 727--737 (1980; Zbl 0475.58005) Full Text: DOI References: [1] Elles, Amer. J. Math. 86 pp 109– (1964) [2] Elles, Bull. London Math. Soc. 10 pp 1– (1978) [3] Misner, Phys. Rev. D 18 pp 4510– (1978) [4] Instantons in nonlinear s-models, gauge theories and general relativity, Preprint, Institut für Theoretische Physiks, Freie Universität, Berlin, 1979. [5] Some problems on the Yang–Mills fields over Riemannian manifolds, Preprint, ITP-SB-79-57, Institute for Theoretical Physics, SUNY at Stony Brook, 1979. [6] Leçons sur la Geometrie des Espaces de Riemann, Gauthier-Villars, Paris, 1928. [7] and , Method of Mathematical Physics, Interscience, New York, 1962. [8] Lectures on Partial Differential Equations, Interscience, New York, 1954. [9] Pohlmeyer, Commun. Math. Phys. 46 pp 207– (1976) [10] Zakharov, JETP Lett. 27 pp 47– (1978) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.