On the uniform convergence of quasiconformal mappings
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- by Bruce Palka PDF
- Trans. Amer. Math. Soc. 184 (1973), 137-152 Request permission
Erratum: Trans. Amer. Math. Soc. 200 (1974), 445-445.
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
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 184 (1973), 137-152
- MSC: Primary 30A60
- DOI: https://doi.org/10.1090/S0002-9947-1973-0340593-4
- MathSciNet review: 0340593