Sobolev Embedding of a Sphere Containing An Arbitrary Cantor Set in the image

Piotr Hajłasz, Xiaodan Zhou

We construct a large class of pathological $n$-dimensional topological spheres in ${\mathbb{R}}^{n+1}$ by showing that for any Cantor set $C\subset {\mathbb{R}}^{n+1}$ there is a top…