Doubling measures, monotonicity, and quasiconformality
经典分析与常微分方程
2007-09-03 v2 度量几何
摘要
We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.
引用
@article{arxiv.math/0611110,
title = {Doubling measures, monotonicity, and quasiconformality},
author = {Leonid V. Kovalev and Diego Maldonado and Jang-Mei Wu},
journal= {arXiv preprint arXiv:math/0611110},
year = {2007}
}
备注
20 pages. Revised to address referee's comments