Doubling measures, monotonicity, and quasiconformality

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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.
20 pages. Revised to address referee's comments

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Classical Analysis and ODEs, Metric Geometry, 30C65; 28A75, 42A55, 47H05

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http://salesiana.dossiersoluciones.com/handle/123456789/137137

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611110
 http://arxiv.org/abs/math/0611110
 Math. Z. 257 (2007), no. 3, 525-545

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arXiv