# On Locally Quasiconformal Teichmuller Spaces

## TL;DR

This paper introduces a generalized Teichmüller space for locally quasiconformal mappings with controlled dilatation growth, establishing existence, uniqueness, and analyzing associated circle maps.

## Contribution

It extends classical Teichmüller theory to a broader class of locally quasiconformal mappings with new existence and uniqueness results.

## Key findings

- Defined a universal Teichmüller space for locally quasiconformal maps
- Proved existence and uniqueness of extremal mappings in this space
- Analyzed the properties of circle maps arising from these mappings

## Abstract

We define a universal Teichm\"uller space for locally quasiconformal mappings whose dilatation grows not faster than a certain rate. Paralleling the classical Teichm\"uller theory, we prove results of existence and uniqueness for extremal mappings in the generalized Teichm\"uller class. Further, we analyze the circle maps that arise.