Update: The G Flex is finally official, with a 6" curved plastic OLED
LG is soon to release its first phone with a flexible OLED display, the G Flex. A few days ago Engadget got hold of some "press renders" showing the upcoming phone, and now Argentinian broadcaster Telefe managed to get hold of the device, showing a video of it in action (the video also includes Samsung's Galaxy Round). Unfortunately I cannot show the video here, but you can watch it at Telefenoticias.
The G Flex will use a 6" flexible OLED display made by LG Display that is curved from top to bottom. I think this makes more sense than Samsung's Galaxy Round which is curved from left to right. From the video you can see that the G Flex has rear-mounted buttons (like in LG's G2). The camera is reportedly 13 mp and that's all we know currently. LG will release the G Flex in Korea soon, and will probably not release it anywhere else (similarly to Samsung).
Earlier this month LGD announced today that it will start mass producing flexible OLEDs for smartphones. The first panel is indeed 6" in size. It weighs just 7.2 grams and is only 0.44 mm thin. LG Display has a flexible OLED 4.5-Gen pilot line that has a capacity of 12,000 monthly sheets, which translates to probably around 200,000 to 300,000 monthly 6" panels (depends on the production yield). LGD will also use this line for R&D so we can assume real production capacity will be very limited at first.