An electronic device may have a hinge that allows the device to be flexed about a bend axis. A display may span the bend axis. The device may have a stainless steel and/or carbon fiber reinforced polymer layer with slots. The slots may overlap the bend axis. The slots may have at least one property that varies in a non-linear manner as a function of position on the layer. The device may include an adhesive layer with a cutout that overlaps the slots. An interface that defines the cutout may have a plurality of recesses with varying depths. A flexible printed circuit may be attached to an edge of the display panel. The display cover layer may overlap a bonding region between the flexible printed circuit and the edge of the display panel. A UV-curable gap filler may be interposed between the flexible printed circuit and the display cover layer.