How tight are the curves ?

Without knowing too much about what you are doing maybe .....

If not super tight or a lot of curves back to back,

set up the rough curve with wood between two sawhorses ( horizontally). Lay the 1/8 drywall flat on the form and lightly spay with water ( lightly! ). Let it sit over night. Remember to use two layers on the wall. (Takes practice )

Second idea ... the backerboard that is used in low end cabinets. Kind of a cross between cardboard and press board. I don't know if that would be thick enough for you. Comes 4' x 8' sheets.

Third idea ... Old fashion plaster. Works great, lasts long time.

Forth idea, backcut wood. Lots of parallel cuts close together ( only works for outside curves ). Kind of like a roll-up door layed on it's side ...

If you can give me an idea of the radius of the curves, how close together they are and if they are inside or outside curves, maybe I can offer some other ideas.

You can take plywood and make a series of cuts through to, but not including, the last ply, then bend it around. For extra strength, put some stuff like liquid nails, epoxy, or whatever in the grooves before bending. Placement of cuts depends on the radius of the curve you are making.

It would be a great help if you could tell us the radius of the curves, and the intended use. Does the material need to be waterproof, temperature resistant, or impact resistant? Is the finished surface rigid or flexible.

I suspect there a many products that will work, but no way to narrow down the list without performance specs.