Korean news site ETNews posted an article discussing Samsung's and LG Display's flexible OLED display plan for 2014. According to the report, LG Display will focus on reducing the size of the OLEDs while increasing the resolution and other display aspects, while Samsung wants to develop new display designs and forms.
LG Display is currently producing a 6" 720p flexible OLED panel - which means a PPI of 245. Samsung's display (5.7", Full-HD) has a much higher PPI of 386. In 2014, LGD hopes to start producing a 5.5" Full-HD panel. The company also reportedly has issues with heat handling and they want to address this issue.
According to the report, Samsung's plans for the near future is to enable different curved designs - so they will have both horizontal and vertical curves. Samsung also wants to enable designs that have curved edges.