Quasiconformal dimensions of self-similar fractals
Quasiconformal dimensions of self-similar fractals
The Sierpinski gasket and other self-similar fractal subsets of \mathbb R^d , d\ge 2 , can be mapped by quasiconformal self-maps of \mathbb R^d onto sets of Hausdorff dimension arbitrarily close to one. In \mathbb R^2 we construct explicit mappings. In \mathbb R^d , d\ge 3 , the results follow …