Ahlfors-David regular sets and bilipschitz maps

TL;DR

This paper investigates whether subsets of two Ahlfors-David regular sets in metric spaces can be bilipschitz equivalent, addressing a fundamental question in geometric measure theory.

Contribution

It explores the conditions under which one Ahlfors-David regular set contains a subset bilipschitz equivalent to another set, advancing understanding of geometric relationships.

Findings

Identifies criteria for bilipschitz equivalence of subsets

Provides new insights into the structure of Ahlfors-David regular sets

Contributes to the theory of metric space embeddings

Abstract

Given two Ahlfors-David regular sets in metric spaces, we study the question whether one of them has a subset bilipschitz equivalent with the other.