TITLE: Classification of 2-dimensional Alexandrov spaces
QUESTION [5 upvotes]: Is it possible to classify explicitly compact 2-dimensional Alexandrov spaces with curvature bounded below (either with or without boundary)?
If yes, a reference would be helpful.
EDIT: If the question is too general, may be one can classify somehow non-negatively curved compact 2-dimensional Alexandrov spaces, e.g. as pieces of convex surfaces (see my comment below). In general I would be interested to know as precise result as possible.

REPLY [5 votes]: Applying doubling theorem, we can get rid of boundary.
Then pass to the universal cover.
The obtained space is isometric to convex surface in the model space with curvature $\kappa$ and any motion of your original space can be extended as a motion of this surface.
So your space is a quotient of convex surface by a discrete group of motions of the model space.
In particular, if your space had a boundary it will be lifted to plane curves in the model space.
In general, the surface is not unique (up to congruence), 
so it is not exactly a classification, but close.