Apple's CEO Tim Cook announced that the company aims to ship their first wearable, the Apple Watch, in April 2015. Officially Apple said that the phone uses a "flexible Retina display", which doesn't really tell us anything regarding the technology, but according to several trusted sources, the Watch uses a flexible OLED display.
It's highly likely that the flexible OLED supplier is LG Display. This has been reported months ago. We reported that Apple may be interested in signing a deal with SDC too for the same flexible OLEDs, but apparently that did not happen.