Degenerate conformal structures

TL;DR

This paper introduces new rectification theorems for degenerate quasi-conformal structures, enabling the analysis of complex quotient spaces and defining unique polynomial renormalizations with Cantor set Julia sets.

Contribution

It provides novel rectification techniques for degenerate structures and applies them to establish unique polynomial renormalizations with Cantor Julia sets.

Findings

New rectification theorems for degenerate quasi-conformal structures

Definition of unique polynomial renormalization for Cantor Julia sets

Framework for analyzing quotient Riemann surfaces with empty interior

Abstract

We present new rectification theorems of degenerate quasi-conformal structures that give a meaning to quotients of Riemann surfaces with empty interior "fundamental domains". These techniques are used to define the unique renormalization of polynomials with Cantor set Julia sets.