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

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

1998-06-03

arxiv.org/abs/math/9806015v1

Mathematics

Complex Variables

29 Pages, 39 PostScript figures

Scientific paper

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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