Non-removable sets for quasiconformal and locally biLipschitz mappings in R3
Abstract
We give an example of a totally disconnected set E in R3 which is not removable for quasiconformal homeomorphisms, i.e., there is a homeomorphism f of R3 to itself which is quasiconformal off E, but not quasiconformal on all of R3. 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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