A1 Journal article (refereed)
Uniformization with Infinitesimally Metric Measures (2021)

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

JYU authors or editors

Publication details

All authors or editors: Rajala, Kai; Rasimus, Martti; Romney, Matthew

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2021

Publication date: 26/05/2021

Volume: 31

Issue number: 11

Pages range: 11445-11470

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-021-00689-y

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/78803

Publication is parallel published: https://arxiv.org/abs/1907.07124

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.

Keywords: complex analysis; measure theory; metric spaces

Free keywords: metric doubling measure; quasiconformal mapping; quasisymmetric mapping; conformal modulus

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2021

JUFO rating: 2