Screen with curved edges is a solution promoted by Samsung. The South Korean company from the moment when Galaxy S6 entered the sale sells also version of their flagship with curved screen on the sides. Such a smartphone holds in your hand in a different way than "standard" phone, and in addition curved sides allow you to set additional options resulting from gestures made on the sides of the screen. It has been said for some time that Samsung is working on improving this idea by introducing a curved screen on four sides. As it turns out, exactly such a project was patented, but unexpectedly it was done by another company than Samsung.
This idea was patented by the Chinese company Xiaomi. In the attached picture we can see how a phone would look with four curved edges. On this photo we can't see front camera, so this may suggest that Xiaomi thinks about creating a solution that allows placing the front camera under the screen in a similar way as Essential plans to do in Essential Phone 2. It is important to remember that from reserving patent to its implementation Xiaomi will have a long way to go, and even we have no guarantee that such an idea will be implemented at all.