2D dilaton gravity made compact
  We show that the equations of motion of two-dimensional dilaton gravity conformally coupled to a scalar field can be reduced to a single non-linear second-order partial differential equation when the coordinates are chosen to coincide with the two scalar fields, the matter field $f$ and the dilaton $\phi$, which are present in the theory. This result may help solve and understand two- and higher-dimensional classical and quantum gravity. 
M. Navarro