Computing boundary extensions of conformal maps

Abstract

Let $\varphi$ be a conformal map of the unit disk onto a domain $D$, and suppose $\varphi$ has a boundary extension. We show that arbitrarily good approximations of the boundary extension of $\varphi$ can be computed from sufficiently good approximations of $\varphi$ and sufficient local connectivity information for the boundary of $D$.

Patches gap in proof of Theorem 3.3

References in corpus (3)

• Effective local connectivity properties
• An effective Caratheodory Theorem
• Computing boundary extensions of conformal maps part 2

Cited by in corpus (1)

• Carathéodory's Theorem and moduli of local connectivity