Touch Display Research released a new report about flexible display technologies (Flexible and Curved Display Technologies and Market Forecast Report). The research company forecasts that the flexible and curved display market will reach $27 billion by 2023:
This report include over 10 display technologies: OLEDs, LCDs, electrophoretic, LED, plasma, electrowetting, electrochromic and more. They have detail break down of the revenue information by 8 technology categories, but I guess it makes sense to assume OLEDs will take the lion share of this market. TDR does mention several curved applications that are already on the market: curved OLED TVs and LCD TVs, smart watches with flexible and curved display (they mention Nike's FuelBand and its curved LED array display).