UBI Research posted an interesting note. The company says that rigid OLED shipments (237 million) command a 79.2% market share of the entire OLED smartphone market, up from 64.5% in 2018.

Rigid vs flexible OLED glass area production (2017-2023, UBI Research)

Display makers have mostly invested in flexible OLED production - but currently there is higher demand for the lower cost rigid OLEDs. All rigid OLED lines are currently in full capacity and UBI suggests that we may see some companies converting flexible OLED lines to rigid OLED production - or that we'll see new investments in rigid OLED production.

The main producer of rigid OLEDs is Samsung Display (in its A1 and A2 lines) but China's Visionox and EDO also produce such displays in lower volume.