# Conformal map from quadrilateral to a sector of a circle [duplicate]

Can anyone advise me on how to derive a conformal map for this mapping? I am familiar with how to apply Schwarz-Christoffel from the upper half plane to the quadrilateral, but how do I then map from the quadrilateral to the sector?

• The map $z \mapsto z^{\alpha}$ maps the disk to a sector. The Cayley mapping takes the upper half plane to the disk. Nov 26 '19 at 11:19
• @Ben McKay Is the mapping above as straightforward as mapping the upper half plane to a sector, considering the existence of vertex B' on the right image? Nov 26 '19 at 13:28