According to Business Korea, Samsung Display is producing a flexible OLED display designed for smartphones. The report indicates the company has invested close to 400 billion won ($325.73 million USD) to date in the project. Apparently, Samsung is expecting to double the production of its curved displays from 15,000 units per month to over 30,000 units early next year.
There has been a couple curved display smartphones release in the market, specifically the LG G Flex and the Samsung Galaxy edge.
[source] Business Korea [/source]
