Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Transactions of the ...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article
Data sources: zbMATH Open
Transactions of the American Mathematical Society
Article . 1984 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1984 . Peer-reviewed
Data sources: Crossref
versions View all 3 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Jordan domains and the universal Teichmüller space

Authors: Barbara Brown Flinn;

Jordan domains and the universal Teichmüller space

Abstract

Let L L denote the lower half plane and let B ( L ) B(L) denote the Banach space of analytic functions f f in L L with ‖ f ‖ L > ∞ {\left \| f \right \|_L} > \infty , where ‖ f ‖ L {\left \| f \right \|_L} is the suprenum over z ∈ L z \in L of the values | f ( z ) | ( t e x t I m z ) 2 \left | {f(z)} \right |{(text{Im} z)^2} . The universal Teichmüller space, T T , is the subset of B ( L ) B(L) consisting of the Schwarzian derivatives of conformal mappings of L L which have quasiconformal extensions to the extended plane. We denote by J J the set \[ { S f : f is conformal in  L and  f ( L ) is a Jordan domain } , \left \{ {{S_f}:f{\text {is conformal in }}L{\text {and }}f(L){\text {is a Jordan domain}}} \right \}, \] which is a subset of B ( L ) B(L) contained in the Schwarzian space S S . In showing S − T ¯ ≠ ∅ S - \bar T \ne \emptyset , Gehring actually proves S − J ¯ ≠ ∅ S - \bar J \ne \emptyset . We give an example which demonstrates that J − T ¯ ≠ ∅ J - \bar T \ne \emptyset .

Keywords

General theory of conformal mappings, quasicircle, Jordan domain, Teichmüller space, Schwarzian derivatives of univalent mappings, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Quasiconformal mappings in the complex plane, Schwarzian derivatives of conformal mappings

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    5
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
bronze