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)

 

On the uniform convergence of quasiconformal mappings


Author: Bruce Palka
Journal: Trans. Amer. Math. Soc. 184 (1973), 137-152
MSC: Primary 30A60
Erratum: Trans. Amer. Math. Soc. 200 (1974), 445-445.
MathSciNet review: 0340593
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let D be a domain in extended Euclidean n-space with ``smooth'' boundary and let $ \{ {f_j}\} $ be a sequence of K-quasiconformal mappings of D into $ {R^n}$ which converges uniformly on compact sets in D to a quasiconformal mapping. This paper considers the question: When does the sequence $ \{ {f_j}\} $ converge uniformly on all of D? Geometric conditions on the domains $ {f_j}(D)$ are given which are sufficient and, in many cases, necessary for uniform convergence. The particular case where D is the unit ball in $ {R^n}$ is examined to obtain analogues to classical convergence theorems for conformal mappings in the plane.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A60

Retrieve articles in all journals with MSC: 30A60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0340593-4
PII: S 0002-9947(1973)0340593-4
Keywords: Quasiconformal mapping, uniform convergence, uniform domain, modulus of a path family, Fréchet distance
Article copyright: © Copyright 1973 American Mathematical Society