PreprintCC BY-NC-SA 4.0arXiv
Local structure of sumsets and projections of self-affine carpets
Abstract
We show that if X and Y are self-similar sets in ℝ with multiplicatively independent contraction ratios, then the Assouad dimension of X+Y is one. As an application, we show that for a large class of self-affine carpets, the Assouad dimension of any non-principal orthogonal projection is one. The latter result is new even for the simplest case of Bedford-McMullen carpets.
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BibTeX
@misc{anttila2026local,
title = {{Local structure of sumsets and projections of self-affine carpets}},
author = {Roope Anttila and Jonathan M. Fraser},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26119},
eprint = {2610.26119},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26119},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Local structure of sumsets and projections of self-affine carpets
AU - Roope Anttila
AU - Jonathan M. Fraser
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26119
UR - https://arxiv.org/abs/2610.26119
AB - We show that if X and Y are self-similar sets in ℝ with multiplicatively independent contraction ratios, then the Assouad dimension of X+Y is one. As an application, we show that for a large class of self-affine carpets, the Assouad dimension of any non-principal orthogonal projection is one. The latter result is new even for the simplest case of Bedford-McMullen carpets.
ER -