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In the similar context as Conformal welding of rectifiable curves In classical conformal welding theory, we start with a homeomorphism $h$ of the unit circle and try to find a Jordan domain $D$ ...

I'm in the middle of a project concerning a Bernoulli-type free boundary problem in $\mathbb{R}^2$ and, as part of this project, I would like to understand the boundary behavior of conformal maps on ...

Let $I\subseteq \mathbb{R}$ an open interval. Let $f:I\rightarrow \mathbb{C}$ real analytic. Suppose we want to numerically compute an analytic extension of $f$. We will assume the following: we are ...

Context. In their paper, "Uniformization and Constructive Analytic Continuation of Taylor Series", Costin and Dunne present a constructive method to greatly increase the accuracy of a ...