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

Christopher J. Bishop
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Abstract

We give an example of a totally disconnected set E in R^3 which is not removable for quasiconformal homeomorphisms, i.e., there is a homeomorphism f of R^3 to itself which is quasiconformal off E, but not quasiconformal on all of 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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Christopher J. Bishop. 1998-06-03. Non-removable sets for quasiconformal and locally biLipschitz mappings in R^3. https://arxiv.org/abs/math/9806015

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