TeichmUller's work on the type problem (To appear in Vol. VII of the Handbook of Teichm{ü}ller theory, 2020)

Vincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos

The type problem is the problem of deciding, for a simply connected Riemann surface, whether it is conformally equivalent to the complex plane or to the unit dic in the complex pla…