Lipschitz surjections between self-similar sets

Attila Gáspár

arXiv:2608.16471v1 Primary: math.MG Secondary: math.CA

Abstract

We give a characterization of the existence of Lipschitz surjections between dust-like self-similar sets of the same dimension under the assumption that the similarity ratios are commensurable. Our results apply more generally to graph-directed fractals.

Disclosure

“ents on an earlier version of the paper. The author was supported by the National Research, Development and Innova- tion Office – NKFIH, grants nos. 146922 and 152822. Declaration of generative AI and AI-assisted technologies OpenAI’s ChatGPT was used to obtain feedback on earlier drafts of this man- uscript, including possible mathematical inaccuracies, missing details, inconsisten- cies in constants and notation, typographical errors, and clear language issues. The mathematic”
PDF page 18

Classification: Rewriting existing author-written text
Multiplier: 4
Verified: 2026-08-23T05:19:58.410343Z

Structural counts

Pages 18 pdf

Theorems 6 source

Lemmas 8 source

Propositions 12 source

Corollaries 1 source

Definitions 5 source

Displayed equations 53 source

Bibliography entries 0 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file gd_lip.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.