Filed in May of this year and made public this month, Samsung's latest patent application details a "method of operating functions of a portable terminal having a bended display." You can think of this as the manual for the crazy prototype shown off by the Korean company at CES in January.
It seemed outlandish then, and still has to prove its viability for a lot of people today, but that wraparound display is very much in Samsung's plans for next year. A Bloomberg report said as much last week, plus the company's 2013 Analyst Day has already committed it to "bended" smartphone displays sometime in 2014 or 2015. The distinguishing feature in Samsung's nomenclature between a curved display, such as on the Galaxy Round, and a so-called bended one appears to be in the severity of the curve. This slide from its recent presentation shows the hierarchy from curved to bended to flexible displays.
Back in January, we only saw a glimpse of the potential uses of a side-screen on your phone, but Samsung's present submission to the US Patent Office is far more detailed and rigorous. Just how useful any of these applications will be, however, must remain a question until they make the transition from paper to a bended reality.