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It is shown in this note that a class of Lagrangian field theories closelyrelated to the wave-map equation and the Skyrme model obeys the dominant energycondition, and hence by Hawking's theorem satisfies finite speed ofpropagation. The subject matter is a generalization of a recent result ofGibbons.

Dominant energy condition and causality for Skyrme-like generalizations of the wave-map equation