# Geodesic surface

1. Jun 6, 2008

### mhill

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 ?,

2. Jun 18, 2008

### gel

I don't know about the general theory, but in Euclidean space this is Plateau's problem.
For space-time surfaces, in Minkowski space, it is similar to the simplest (non-quantized) string theory except I assume you would be maximizing the "area".

3. Jun 19, 2008