Oh, almost forgot. New paper on arXiv.

Gary Gibbons showed via explicit computations using eigenvalues that the Skyrmion equation obeys the dominant energy condition. In my paper, I proved the dominant energy condition for a class of Lagrangian field theories, of which the Skyrmion model and the wave-map equations are special subsets. The trick is to observe that the Lagrangian for the equations have very geometric interpretations, which vastly simplifies the computation for the stress-energy tensor. In this language, the structure of the stress-energy tensor becomes completely analogous to the stress-energy tensor for the homogeneous wave equation, and dominant energy condition follows simply.