Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Metric Geometry
2026-01-21 v1
Abstract
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type fractal space is attained. The attaining metrics are constructed explicitly. This gives new examples of attainment and clarifies the possible obstructions.
Keywords
Cite
@article{arxiv.2601.14241,
title = {Conformal dimension and its attainment on self-similar Laakso-type fractal spaces},
author = {Riku Anttila and Sylvester Eriksson-Bique and Lassi Rainio},
journal= {arXiv preprint arXiv:2601.14241},
year = {2026}
}
Comments
41 pages, 4 figures. Comments are welcome!