Doubling measures, monotonicity, and quasiconformality

Leonid V. Kovalev; Diego Maldonado; Jang Mei Wu

doi:10.1007/s00209-007-0132-5

Doubling measures, monotonicity, and quasiconformality

Leonid V. Kovalev, Diego Maldonado, Jang Mei Wu

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	525-545
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	257
Issue number	3
DOIs	https://doi.org/10.1007/s00209-007-0132-5
State	Published - Nov 2007
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-007-0132-5

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AB - 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.

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Doubling measures, monotonicity, and quasiconformality

Abstract

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