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Cartesian products of Sierpiński carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the Sierpiński carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesia…
Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio
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 Ahlfor…
Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Ryosuke Shimizu
We construct self-similar -energy forms on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{…
The Combinatorial Loewner Property and super-multiplicativity inequalities for symmetric self-similar metric spaces
Riku Anttila, Sylvester Eriksson-Bique
This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the Sierpiński carp…
On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property
Riku Anttila, Sylvester Eriksson-Bique
The combinatorial Loewner property was introduced by Bourdon and Kleiner as a quasisymmetrically invariant substitute for the Loewner property for general fractals and boundaries o…