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arXiv · 2601.14241

Conformal dimension and its attainment on self-similar Laakso-type fractal spaces

Riku Anttila·Sylvester Eriksson-Bique·Lassi Rainio
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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.

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Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio. 2026-01-20. Conformal dimension and its attainment on self-similar Laakso-type fractal spaces. https://arxiv.org/abs/2601.14241

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