Are you wanting bowed doors on the front?
Here's a video of a guy that makes a bent chair leg out of plywood. For doors it would likely be a simular process but with more clamps etc.
YouTube - Bent plywood in 7 easy steps.
I know of guys that bend sheets of plywood by soaking it in water for a long time and slowly bending it to shape using a form and a bunch of clamps as well.
Of course i wouldn't trust the bent sections of the plywood to hold any significant amount of weight after soaking and bending etc.
Interestingly enough, my brother in-law just finished builting us a fireplace out of concrete that has some very smooth curves etc and that is entirely hollow and very light (only took two of us to lift the bottom and top sections into the house), yet it's still rated for 4000 psi of weight. Would be interesting to see if he could built a stand with a simular method.
Edit: Just thought of an idea to make the doors. Use the method in the video and then use a biscuit joiner to join the sections together to make a full sized door for the cabnet. See Biscuit joiner - Wikipedia, the free encyclopedia
for more info on what a biscuit joiner if you don't know what one is.