Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1988-0920148-1
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 ${4^{1 - {K^2}}}|x{|^K} \leqslant |f(x)| \leqslant {4^{1 - 1/{K^2}}}|x{|^{1/K}}$ 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

Article copyright: © Copyright 1988 American Mathematical Society