Following Samsung's success with curved-edge smartphones, other phone makers are obviously thinking about similar designs. It turns out that LG has filed for several US trademarks last week, all of which hint at phones with curved edges.
The trademarks include G Edge, Super Edge, Dual Edge, Double Edge and Dual Side Edge. The G Edge seems to be the best name for LG's first curved-edge flexible OLED phone, and will complement the company's G Flex 2 smartphone which is a vertically-curved flexible OLED smartphone.
In January 2015 during CES, LG Display unveiled a phone prototype that uses a 6" plastic-OLED display that is curved on both edges (you can see the prototype above). LGD called that panel an "Active Bending" panel.
The prototype had a 1280x720 resolution and offered a brightness of 300 nits. These aren't very exciting specs (Samsung's 5.7" flexible OLED in the GS6 edge+, for example, offers a resolution of 2560x1440 and 861 nits) but it's likely that LGD can produce better OLEDs now.