Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A remark on angular complex dilatations of quasiconformal mappings

Author: Richard Fehlmann
Journal: Proc. Amer. Math. Soc. 104 (1988), 1071-1077
MSC: Primary 30C60; Secondary 30C75
MathSciNet review: 930251
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: By a theorem of Ortel an angular complex dilatation $ \kappa $ is extremal iff it is Teichmüllèr (quadratic differential with finite norm) or if it satisfies an integral condition involving the angular limits $ {\lambda _x}(\vartheta )$. We show that this second case occurs iff $ {\lambda _x}(\vartheta )$ can be given explicitly at a certain point $ x$, namely by $ {\lambda _x}(\vartheta ) = {\left\Vert \kappa \right\Vert _\infty }{e^{2i}}(\vartheta - {\vartheta _0})$. Moreover, we investigate this statement under the weaker condition of angularity when the uniformity part in its definition is dropped.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C60, 30C75

Retrieve articles in all journals with MSC: 30C60, 30C75

Additional Information

PII: S 0002-9939(1988)0930251-3
Article copyright: © Copyright 1988 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia