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.



Classification of 2-dimensional Alexandrov spaces
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.


