# Geodesic surface

if we have or can have geodesic curves minimizing the integral $$\sqrt (g_{ab}\dot x_a \dot x_b )$$ is there a theory of 'minimizing surfaces or Geodesic surfaces' that minimize the Area or a surface ?,

I don't know about the general theory, but in Euclidean space this is http://en.wikipedia.org/wiki/Plateau%27s_problem" [Broken].
For space-time surfaces, in Minkowski space, it is similar to the simplest (non-quantized) http://en.wikipedia.org/wiki/Nambu-Goto_action" [Broken] except I assume you would be maximizing the "area".

Last edited by a moderator:
robphy