  Any surface is completely characterized by a metric and a symmetric tensor
satisfying the Gauss-Codazzi-Mainardi equations (GCM), which identifies the
latter as its curvature. We demonstrate that physical questions relating to a
surface described by any Hamiltonian involving only surface degrees of freedom
can be phrased completely in terms of these tensors without explicit reference
to the ambient space: the surface is an emergent entity. Lagrange multipliers
are introduced to impose GCM as constraints on these variables and equations
describing stationary surface states derived. The behavior of these multipliers
is explored for minimal surfaces, showing how their singularities correlate
with surface instabilities.
