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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Capacity densities and angular limits of quasiregular mappings


Author: Matti Vuorinen
Journal: Trans. Amer. Math. Soc. 263 (1981), 343-354
MSC: Primary 30C60
MathSciNet review: 594412
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Abstract: It is shown that if a bounded quasiregular mapping of the unit ball $ {B^n} \subset {R^n}$, $ n \geqslant 2$, has a limit at $ b \in \partial {B^n}$ through a set $ E \subset {B^n}$ with $ b \in \bar E$, then it has an angular limit at $ b$ provided that $ E$ is contained in an open cone $ C \subset {B^n}$ with vertex $ b$ and that $ E$ is thick enough at $ b$. The thickness condition is expressed in terms of the $ n$-capacity density.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0594412-6
Keywords: Quasiconformal and quasiregular mappings, boundary behavior, angular limits
Article copyright: © Copyright 1981 American Mathematical Society