The phablet Galaxy Note 4 was launched at IFA 2014 alongside a variant Galaxy Note Edge with a display stretching to one of the edges, thanks to the new possibilities of flexible screens.
It will probably not be very long before the Korean giant unveils a device whose screen would stretch on the two side edges and maybe it's a Galaxy S6 Edge derived from its next benchmark smartphone which could be the ideal candidate.
If its existence remains questionable, a patent obtained by the Korean manufacturer and highlighted by the site Patently mobile describes a smartphone whose display stretches over the edges and to the back. The additional display allows notifications to appear even when the smartphone is placed on the screen.
It remains a general patent describing a concept which will not necessarily be applied, or which will not be before the technologies are really available. It nevertheless gives an idea of the general direction that Samsung could take for these future terminals, breaking away from the traditional black rectangle and its flat slab which remains the archetype of the smartphone currently.