LG presents an update on its "real" curved smartphone, the G Flex, at CES 2015-- the G Flex2, a handset featuring the same "dynamically curved" design if with a smaller display and various internal improvements.
As mentioned earlier, in a perhaps surprising move the G Flex2 is smaller than its predecessor, as it features a 5.5-inch (the original G Flex was 6-inch) 1920x1080 P-OLED display. As for the display curvature LG describes it as nothing less than "a symphony of curves ranging from a radius of 400mm to 700mm across the front, back, sides and top-to-bottom edges."
Also making a return is the "self healing" back cover, one the company claims recovers even faster from nicks and scratches.