Apple files patent application for an Apple iPhone with wrap-around AMOLED display
The patent also discusses the radio transparency of the glass, allowing for the transmission of radio signals. This could be beefed up by the use of metal structures in certain areas of the device. The display would get help from facial recognition technology (using a front-facing camera) to help correctly orient the content on the display. In addition, the patent talks about multiple layers of the display positioned in such a manner that it would create 3D images. One of the iterations of the device mentioned in the patent would allow users to remove end caps on a tube-shaped unit to connect it with another tube-shaped model, forming a larger display.
source: USPTO via AppleInsider