The Heinonen-Semmes problems after thirty years

TL;DR

This paper reviews the progress made over thirty years on the Heinonen-Semmes problems related to mappings, measures, and metrics in conformal geometry and dynamics.

Contribution

It provides a comprehensive survey of the developments and current status of the original thirty-three questions posed by Heinonen and Semmes.

Findings

Summary of key advances in the field

Identification of unresolved questions

Overview of techniques used in recent research

Abstract

We survey the current status of the questions posed by Juha Heinonen and Stephen Semmes in `Thirty-three yes or no questions about mappings, measures, and metrics' (Conformal Geometry and Dynamics, 1997).