Generalized quasidisks and conformality: progress and challenges

TL;DR

This paper surveys recent advances in the theory of generalized quasidisks, highlighting progress, minor improvements, and open questions in the field of conformality and geometric function theory.

Contribution

It provides a comprehensive overview of recent developments in generalized quasidisks and offers some minor technical improvements and open questions.

Findings

Summarizes recent progress in generalized quasidisks

Provides minor technical improvements on existing results

Poses open questions in the field

Abstract

In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were posed.