Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sharp distortion theorems for quasiconformal mappings


Authors: G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen
Journal: Trans. Amer. Math. Soc. 305 (1988), 95-111
MSC: Primary 30C60; Secondary 30C75
MathSciNet review: 920148
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Continuing their earlier work on distortion theory, the authors prove some dimension-free distortion theorems for $ K$-quasiconformal mappings in $ {R^n}$. For example, one of the present results is the following sharp variant of the Schwarz lemma: If $ f$ is a $ K$-quasiconformal self-mapping of the unit ball $ {B^n}$, $ n \geqslant 2$, with $ f(0) = 0$, then $ {4^{1 - {K^2}}}\vert x{\vert^K} \leqslant \vert f(x)\vert \leqslant {4^{1 - 1/{K^2}}}\vert x{\vert^{1/K}}$ for all $ x$ in $ {B^n}$.


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


Similar Articles

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

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


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0920148-1
PII: S 0002-9947(1988)0920148-1
Article copyright: © Copyright 1988 American Mathematical Society