Non-removable sets for quasiconformal and locally biLipschitz mappings in R^3
复变函数
2007-05-23 v1 经典分析与常微分方程
摘要
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.
引用
@article{arxiv.math/9806015,
title = {Non-removable sets for quasiconformal and locally biLipschitz mappings in R^3},
author = {Christopher J. Bishop},
journal= {arXiv preprint arXiv:math/9806015},
year = {2007}
}
备注
29 Pages, 39 PostScript figures