## Math Problem Statement

prove the Riemann mapping theorem

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Complex Analysis

Conformal Mapping

Holomorphic Functions

### Formulas

T(z) = e^{iθ} (z - a) / (1 - āz)

### Theorems

Riemann Mapping Theorem

Carathéodory-Osgood Theorem

Schwarz Lemma

Dirichlet’s Principle

Carathéodory Extension Theorem

### Suitable Grade Level

Undergraduate - Advanced

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