University of Jyväskylä | JYX Digital Repository

  • English  | Give feedback |
    • suomi
    • English
 
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
View Item 
  • JYX
  • Artikkelit
  • Matemaattis-luonnontieteellinen tiedekunta
  • View Item
JYX > Artikkelit > Matemaattis-luonnontieteellinen tiedekunta > View Item

Uniformization of two-dimensional metric surfaces

ThumbnailFinal Draft
View/Open
592.8 Kb

Downloads:  
Show download detailsHide download details  
Rajala, K. (2017). Uniformization of two-dimensional metric surfaces. Inventiones mathematicae, 207(3), 1301-1375. https://doi.org/10.1007/s00222-016-0686-0
Published in
Inventiones mathematicae
Authors
Rajala, Kai
Date
2017
Discipline
MatematiikkaMathematics
Copyright
© Springer-Verlag Berlin Heidelberg 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.

 
We establish uniformization results for metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover, we show that if such a QC parametrization exists, then the dilatation can be bounded by 2. As an application, we show that the Euclidean upper bound for measures of balls is a sufficient condition for the existence of a 2-QC parametrization. This result gives a new approach to the Bonk-Kleiner theorem on parametrizations of Ahlfors 2-regular spheres by quasisymmetric maps.
Publisher
Springer
ISSN Search the Publication Forum
0020-9910
Keywords
metric surfaces
DOI
https://doi.org/10.1007/s00222-016-0686-0
URI

http://urn.fi/URN:NBN:fi:jyu-201702141437

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/26186503

Metadata
Show full item record
Collections
  • Matemaattis-luonnontieteellinen tiedekunta [4955]

Related items

Showing items with similar title or keywords.

  • Uniformization of metric surfaces using isothermal coordinates 

    Ikonen, Toni (Suomen matemaattinen yhdistys ry, 2022)
    Todistamme metristen pintojen uniformisaatiolauseen. Metrinen pinta on topologinen pinta varustettuna etäisyysfunktiolla, jonka kaksiulotteinen Hausdorffin mitta on lokaalisti äärellinen. Tutkimme milloin metrinen pinta ...
  • Studies of two-dimensional and three-dimensional phononic crystal structures 

    Tian, Yolan (University of Jyväskylä, 2016)
    This thesis focuses on studying phononic crystal structures. More specifically, it is aimed at fabrication and measurement of thermal properties of two-dimensional (2D) periodic microstructures and three-dimensional (3D) ...
  • The impact of two-dimensional perfectionism on burnout and eating disorders in young Finnish athletes : comparison between males and females 

    Sorkkila, Matilda (2014)
    Matilda Sorkkila, 2014. The impact of two-dimensional perfectionism on burnout and eating disorders in young Finnish athletes: comparison between males and females. Master’s Thesis in Sport and Exercise Psychology. Department ...
  • Universal computation by finite two-dimensional coupled map lattices 

    Orponen, Pekka; Matamala, Martin (New England Complex Systems Institute, 1996)
  • Growth of two-dimensional Au patches in graphene pores : a density-functional study 

    Antikainen, Saku (2016)
    Grafeenin löytämisen myötä kaksiulotteisten (2D) materiaalien tutkimus on edennyt huomattavasti viimeisen vuosikymmenen aikana. Myös 2D-metalleja on tutkittu, ja esimerkiksi atominpaksuinen rautakerros on onnistuttu ...
  • Browse materials
  • Browse materials
  • Articles
  • Conferences and seminars
  • Electronic books
  • Historical maps
  • Journals
  • Tunes and musical notes
  • Photographs
  • Presentations and posters
  • Publication series
  • Research reports
  • Research data
  • Study materials
  • Theses

Browse

All of JYXCollection listBy Issue DateAuthorsSubjectsPublished inDepartmentDiscipline

My Account

Login

Statistics

View Usage Statistics
  • How to publish in JYX?
  • Self-archiving
  • Publish Your Thesis Online
  • Publishing Your Dissertation
  • Publication services

Open Science at the JYU
 
Data Protection Description

Accessibility Statement

Unless otherwise specified, publicly available JYX metadata (excluding abstracts) may be freely reused under the CC0 waiver.
Open Science Centre