Institute for Mathematical Sciences

Preprint ims98-6

C. Bishop
Non-removable sets for quasiconformal and locally biLipschitz mappings in R^3

Abstract: We give an example of a totally disconnected set $E \subset {\Bbb R}^3$ which is not removable for quasiconformal homeomorphisms, i.e., there is a homeomorphism $f$ of ${\Bbb R}^3$ to itself which is quasiconformal off $E$, but not quasiconformal on all of ${\Bbb R}^3$. The set $E$ may be taken with Hausdorff dimension $2$. The construction also gives a non-removable set for locally biLipschitz homeomorphisms.
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