# Tagged Questions

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### How far do conjugated Mobius transforms move points?

I start with an automorphism $f$ of the complex unit disc $S^1 = \{ z \in \mathbb{C} : |z| \leq 1\}$. I assume that such a map is given by a Mobius transform, namely
$$
f(z) = \frac{z - ...

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### Inverse “Riemann mapping” [closed]

The Riemann mapping theorem states, that any simply connected domain $U \subset \mathbb C$ can be conformally mapped to the open unit disk $D$. I.e. there is a Diffeomorphism $\Psi: D \to U$ such that ...

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### Can one use Brownian motion to prove that two manifolds are not conformally equivalent?

Let me start by a very simple example; consider the following question:
"Let D1 be a square and D2 a rectangle (boundary included). View them
as subsets of the complex plane. Does there exist a ...

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### Conformal Welding Reference

I'm looking for a reference for the following fact: given two Riemann surfaces and an identification of their boundaries, once I topologically glue the surfaces together there exists a unique ...

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### Errata in “Conformal Mapping: Method and Applications” from Schinzinger

hi,
i'm studying the book "Conformal Mapping: Method and Applications" from Schinzinger and more precisely the chapter 6 concerning non-planar field.
In section 6.1.3 the author proposes to solve a ...