The best way to bend carpet over a curve is to cut a "^" into the carpet just to the point where the narrowest part of the "V" hits the part where you bend it down over the front that will give a nice clean edge. Its a bit tricky at first but once you get it right it looks clean. I did it on my stairs for my riser that have two curved ends.
I suppose if the curve of the stage facing is a sharp enough curve, you will have overlap that will need cutting out. I was thinking about how I was doing mine... the face does not curve that much with it being 19.5' wide, but it still may be an minor issue.