Uniformization with Infinitesimally Metric Measures
Abstract
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces X homeomorphic to R2R2. Given a measure μμ on such a space, we introduce μμ-quasiconformal maps f:X→R2f:X→R2, whose definition involves deforming lengths of curves by μμ. We show that if μμ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a μμ-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202111265810Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-021-00689-y
Language
English
Published in
Journal of Geometric Analysis
Citation
- Rajala, K., Rasimus, M., & Romney, M. (2021). Uniformization with Infinitesimally Metric Measures. Journal of Geometric Analysis, 31(11), 11445-11470. https://doi.org/10.1007/s12220-021-00689-y
License
Additional information about funding
Open access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2021