The Schwarz-Christoffel transformation is given by: $$w=\int^z_0 (\epsilon-x_1)^{\frac{\theta_1}{\pi}-1}(\epsilon-x_2)^{\frac{\theta_2}{\pi}-1}...(\epsilon-x_N)^{\frac{\theta_N}{\pi}-1}d\epsilon$$ I understand why this maps the real axis onto a polygon, but I cannot see why the upper half plane must be on the interior of this polygon. Is their an easy way to see this?
2026-04-01 12:20:03.1775046003
Schwarz-Christoffel transformation why to inside?
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