Bending tool for glass panes

A bending tool for bending at least one glass pane by means of suction, the bending tool comprising:

• a frame-like, convex contact surface;
• and
• a cover having a peripheral air guide plate that surrounds the convex contact surface at least in regions,
• wherein the bending tool is configured to generate:
• a first, reduced pressure in a first pressure region between the peripheral air guide plate and the convex contact surface,
• a second, reduced pressure in a second pressure region, wherein the second pressure is less than the first pressure, and
• a third pressure in a third pressure region, wherein the third pressure is greater than the first pressure,
• wherein the bending tool is constructed and arranged to contact a peripheral portion of a main surface of the glass pane such that a majority of the main surface of the glass pane is without contact with the bending tool during bending of the glass pane by the bending tool, and wherein the convex contact surface contacts said peripheral portion during the bending.