According to MacRumors, Apple is planning to release at the least 3 new iPhones next year. This would include a high-end model with a 5.5+ inch OLED screen that is curved on both sides just like the Galaxy S7 Edge and Note 7. The other two models will be the same flat LCD panels. Samsung is expected to even be the main supplier of the OLED curved displays. Foxconn has been making glass casings and OLED displays for next year.
With the height of a 5.5″ iPhone, a 5.8″ display would leave an extra 7.25mm on the left and right sides.