Lipschitz equivalence of subsets of self-conformal sets

TL;DR

This paper establishes conditions under which Lipschitz equivalence of positive measure subsets of self-conformal sets implies a bilipschitz map between the entire sets.

Contribution

It provides new sufficient conditions linking subset Lipschitz equivalence to full set bilipschitz mappings for self-conformal sets.

Findings

Lipschitz equivalence of subsets implies bilipschitz maps between whole sets under certain conditions.

The paper identifies specific criteria for self-conformal sets.

Results extend understanding of geometric structure of self-conformal fractals.

Abstract

We give sufficient conditions to guarantee that if two self-conformal sets E and F have Lipschitz equivalent subsets of positive measure, then there is a bilipschitz map of E into, or onto, F.