Device and method for press bending glass panes

A device for bending glass panes, includes a lower press-bending mould with a frame-shaped contact surface, an upper press-bending mould arranged opposite the contact surface, wherein the lower press-bending mould and the upper press-bending mould are suitable for reshaping a glass pane situated therebetween by pressing, wherein the side edge of the glass pane rests on the contact surface along a contact line, wherein during pressing, the contact line migrates from a first contact line all the way to a pressing line, and wherein the contact surface between the first contact line and the pressing line is convexly curved.