This patent application from Apple looks very similar to Samsung's Galaxy Edge display
The patent suggests that flexible, touch-sensitive OLED displays could be bent to fit multiple edges of electronic devices like tablets or smartphones. Those edge displays could have a range of functions, acting as virtual buttons or switches as well as displaying information.
The application looks to be a continuation of several similar patents though, the first of which was submitted in September 2011.
Here's an image from the patent:
The way the screen functions would depend on what the iPhone was being used for. For example, if you were listening to music, the edge of the iPhone could display a list of songs, artists or albums, and let you scroll through. The section comprised of virtual buttons could then let you change volume or switch between songs.
If the iPhone was being used as a camera, the virtual buttons and switches could let you zoom, turn on the flash, or switch between taking a photo or video.
The display would also let you switch between basic applications.
It's not entirely clear from the application whether these side displays would also show alerts like Samsung's new display does. But the rest of the application looks pretty similar.
Like on Samsung's phone, the patent application shows a display meant to wrap around most of the device.
Since Apple doesn't always create the ideas it patents, there's no guarantee we'll see a wraparound screen on the iPhone in the future, or that this will add to the patent fight between the two smartphone giants.