Bending of glass sheets comprising localized cooling

A device and a process for manufacturing a bent individual glass sheet including a peripheral compression belt, wherein the process includes the heating thereof to its bending temperature in a furnace, the individual bending thereof, and the general cooling thereof. One zone of the sheet at least partially inside the peripheral compression belt, referred to as locally cooled zone, undergoes, after the heating of the sheet, a local cooling faster than the general cooling, when the sheet is at a temperature of at least 530° C. The cutting of the sheet on the locally cooled zone creates edges having edge compressive stresses.