# Is there a Teichm\"uller principle in higher dimensions?

## TL;DR

This paper explores extending Teichmüller's principle, which links extremal problems to quadratic differentials in one complex variable, to higher dimensions using the Loewner differential equation.

## Contribution

It proposes a potential framework for generalizing Teichmüller's principle to several complex variables via the Loewner differential equation.

## Key findings

- Suggests a new approach to higher-dimensional Teichmüller theory
- Connects extremal problems with differential equations in multiple variables
- Provides a foundation for future research in complex analysis

## Abstract

The underlying theme of Teichm\"uller's papers in function theory is a general principle which asserts that every extremal problem for univalent functions of one complex variable is connected with an associated quadratic differential. The purpose of this paper is to indicate a possible way of extending Teichm\"uller's principle to several complex variables. This approach is based on the Loewner differential equation.