Royole, a startup established in the US in 2012, unveils their first prototype, a 0.01 mm thick (thin?) flexible AMOLED prototype (which they say is the thinnest ever). Here's a video showing the display in action, it's really cool how it flaps in the wind:

http://www.oled-info.com/royole-shows-001-mm-thick-flexible-amoled-prototype

The company develops flexible AMOLED backplanes - they will not produce such a display, but this is a cool precursor to what may be achieved in a few years.