Remark on the classical solution of the Chaplygin gas as d-branes

The classical solution of a bosonic d-brane in $\mathrm{}(d+1,1\mathrm{})\mathrm{}$ space-time is studied. We work with the light-cone gauge and reduce the problem into a Chaplygin gas problem. The static equation is equivalent to the vanishing of the extrinsic mean curvature, which is similar to Einstein’s equation in vacuum. We show that the d-brane problem in this gauge is closely related to the plateau problem, and we give some nontrivial solutions from minimal surfaces. The solutions of $d-1,d,d+1$ spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of the plateau problem. In addition we discuss the relation to the Hamiltonian-BRST formalism for d-branes.