Surface motions and fluid dynamics

A certain class of surface motions, including those of a relativistic membrane minimizing the three-dimensional volume swept out in Minkowski space, is shown to be equivalent to three-dimensional steady-state irrotational inviscid isentropic gas dynamics. The SU(∞) Nahm equations turn out to correspond to motions where the time t at which the surface moves through the point r is a harmonic function of the three space coordinates. This solutions also implies the linearisation of a non-trivial-looking scalar field theory.