A Set Containing Recfiable Arcs QC-locally But Not QC-globally
Christopher J. Bishop · Pure and Applied Mathematics Quarterly · 2011
We construct a Sierpinski carpet E ⊂ R 2 of area zero and a K 0 > 1 with the property that every K 0 -quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves.